United States v. Ulbricht , 858 F.3d 71 ( 2017 )


Menu:
  • 15-1815-cr
    United States of America v. Ulbricht
    UNITED STATES COURT OF APPEALS
    FOR THE SECOND CIRCUIT
    August Term, 2016
    (Argued: October 6, 2016 Decided: May 31, 2017)
    Docket No. 15-1815
    UNITED STATES OF AMERICA,
    Appellee,
    — v. —
    ROSS WILLIAM ULBRICHT, a/k/a DREAD
    PIRATE ROBERTS, a/k/a SILK ROAD,
    a/k/a SEALED DEFENDANT 1, a/k/a DPR,
    Defendant-Appellant.
    Before:
    NEWMAN, LYNCH, and DRONEY, Circuit Judges.
    Ross William Ulbricht appeals from a judgment of conviction and sentence
    to life imprisonment entered in the United States District Court for the Southern
    District of New York (Katherine B. Forrest, J.), for drug trafficking and other
    crimes associated with his creation and operation of an online marketplace
    known as Silk Road. He argues that (1) the district court erred in denying his
    motion to suppress evidence obtained in violation of the Fourth Amendment;
    (2) the district court committed several errors that deprived him of his right to a
    fair trial, and incorrectly denied his motion for a new trial; and (3) his life
    sentence is both procedurally and substantively unreasonable. For the reasons set
    forth below, the judgment of the district court is AFFIRMED in all respects.
    JOSHUA L. DRATEL, Joshua L. Dratel, P.C., New York, NY, for
    defendant-appellant Ross William Ulbricht.
    EUN YOUNG CHOI, Assistant United States Attorney (Michael
    D. Neff, Timothy T. Howard, Adam S. Hickey, Assistant
    United States Attorneys, on the brief), for Preet Bharara,
    United States Attorney for the Southern District of New
    York, New York, NY.
    Tamar Todd, Jolene Forman, Drug Policy Alliance, Oakland,
    CA, for amici curiae Drug Policy Alliance, Law
    Enforcement Against Prohibition, JustLeadershipUSA,
    and Nancy Gertner.
    Joel B. Rudin, Law Offices of Joel B. Rudin, P.C., New York,
    NY; Steven R. Morrison, University of North Dakota
    School of Law, Grand Forks, ND, for amicus curiae
    National Association of Criminal Defense Lawyers.
    GERARD E. LYNCH, Circuit Judge:
    Defendant Ross William Ulbricht appeals from a judgment of conviction
    and sentence to life imprisonment entered in the United States District Court for
    the Southern District of New York (Katherine B. Forrest, J.). A jury convicted
    Ulbricht of drug trafficking and other crimes associated with his creation and
    2
    operation of Silk Road, an online marketplace whose users primarily purchased
    and sold illegal goods and services. He challenges several aspects of his
    conviction and sentence, arguing that (1) the district court erred in denying his
    motion to suppress evidence assertedly obtained in violation of the Fourth
    Amendment; (2) the district court committed numerous errors that deprived him
    of his right to a fair trial, and incorrectly denied his motion for a new trial; and
    (3) his life sentence is both procedurally and substantively unreasonable. Because
    we identify no reversible error, we AFFIRM Ulbricht’s conviction and sentence in
    all respects.
    BACKGROUND
    In February 2015, a jury convicted Ross William Ulbricht on seven counts
    arising from his creation and operation of Silk Road under the username Dread
    Pirate Roberts (“DPR”).1 Silk Road was a massive, anonymous criminal
    1
    The seven crimes of conviction were: (1) distribution and aiding and abetting
    distribution of narcotics, 21 U.S.C. § 812, § 841(a)(1), § 841(b)(1)(A) and 18 U.S.C.
    § 2; (2) using the Internet to distribute narcotics, 21 U.S.C. § 812, § 841(h) and
    § 841(b)(1)(A); (3) conspiracy to distribute narcotics, 21 U.S.C. § 846; (4) engaging
    in a continuing criminal enterprise, 21 U.S.C. § 848(a); (5) conspiring to obtain
    unauthorized access to a computer for purposes of commercial advantage and
    private financial gain and in furtherance of other criminal and tortious acts, 18
    U.S.C. § 1030(a)(2) and § 1030(b); (6) conspiring to traffic in fraudulent
    identification documents, 18 U.S.C. § 1028(f); and (7) conspiring to launder
    money, 18 U.S.C. § 1956(h).
    3
    marketplace that operated using the Tor Network, which renders Internet traffic
    through the Tor browser extremely difficult to trace.2 Silk Road users principally
    bought and sold drugs, false identification documents, and computer hacking
    software. Transactions on Silk Road exclusively used Bitcoins, an anonymous but
    traceable digital currency.3 The site also contained a private message system,
    which allowed users to send messages to each other (similar to communicating
    via email), a public forum to discuss topics related to Silk Road, and a “wiki,”
    which is like an encyclopedia that users could access to receive advice about
    using the site. Silk Road customers and vendors could also access a support
    2
    Tor is short for the “The Onion Router.” The Tor Network is “a special network
    on the Internet designed to make it practically impossible to physically locate the
    computers hosting or accessing websites on the network.” App’x 53. The Tor
    Network can be accessed via the Tor browser using software that anyone may
    obtain for free on the Internet.
    3
    Bitcoins allow vendors and customers to maintain their anonymity in the same
    way that cash does, by transferring Bitcoins between anonymous Bitcoin
    accounts, which do not contain any identifying information about the user of
    each account. The currency is “traceable” in that the transaction history of each
    individual Bitcoin is logged in what is called the blockchain. The blockchain
    prevents a person from spending the same Bitcoin twice, allowing Bitcoin to
    operate similarly to a traditional form of currency. Bitcoin is also a completely
    decentralized currency, operating free of nation states or central banks; anyone
    who downloads the Bitcoin software becomes part of the Bitcoin network. The
    blockchain is stored on that network, and the blockchain automatically “self-
    updates” when a Bitcoin transaction takes place. Tr. 160.
    4
    section of the website to seek help from the marketplace’s administrators when
    an issue arose.
    According to the government, between 2011 and 2013, thousands of
    vendors used Silk Road to sell approximately $183 million worth of illegal drugs,
    as well as other goods and services. Ulbricht, acting as DPR, earned millions of
    dollars in profits from the commissions collected by Silk Road on purchases. In
    October 2013, the government arrested Ulbricht, seized the Silk Road servers,
    and shut down the site.
    I.    Silk Road Investigation
    After Ulbricht created Silk Road in 2011, the site attracted the interest of at
    least two separate divisions of the Department of Justice:4 the United States
    Attorney’s Offices for the District of Maryland and for the Southern District of
    New York. Throughout the investigations, law enforcement agents knew that the
    person using Dread Pirate Roberts as his or her Silk Road username had created
    and managed the site, but they did not know DPR’s actual identity. In 2012 and
    2013, agents from both offices investigated several individuals who the
    4
    The government first learned of Silk Road and began investigating it in 2011
    after international packages containing drugs were intercepted at Chicago’s
    O’Hare airport.
    5
    government suspected were operating Silk Road as DPR. Those individuals
    included Ulbricht, Anand Athavale, and Mark Karpeles. Ultimately, the New
    York office identified Ulbricht as DPR, but the Maryland office had investigated
    and later abandoned the theory that either Athavale or Karpeles might have been
    Dread Pirate Roberts.
    Two aspects of the pre-arrest investigation into Ulbricht are particularly
    relevant to this appeal: (1) the pen/trap orders that the government obtained to
    monitor Internet Protocol (“IP”) address traffic to and from various devices
    associated with Ulbricht; and (2) the corrupt behavior of two Baltimore agents
    who worked on the Silk Road investigation.
    A. The Pen/Trap Orders
    In September 2013, after Ulbricht became a primary suspect in the DPR
    investigation, the government obtained five “pen/trap” orders. See 18 U.S.C.
    §§ 3121-27 (“Pen/Trap Act”). The orders authorized law enforcement agents to
    collect IP address data for Internet traffic to and from Ulbricht’s home wireless
    router and other devices that regularly connected to Ulbricht’s home router.
    According to the government’s applications for the pen register and trap and
    trace device, “[e]very device on the Internet is identified by a unique number”
    6
    called an IP address. S.A. 73.5 “This number is used to route information between
    devices, for example, between two computers.” 
    Id. at 73-74.
    In other words, an
    “IP address is analogous to a telephone number” because “it indicates the online
    identity of the communicating device without revealing the communication’s
    content.” 
    Id. at 74.
    Ulbricht does not dispute that description of how IP addresses
    function.
    The pen/trap orders thus did not permit the government to access the
    content of Ulbricht’s communications, nor did the government “seek to obtain[]
    the contents of any communications.” 
    Id. at 75.
    According to Ulbricht, the
    government’s use of his home Internet routing data violated the Fourth
    Amendment because it helped the government match Ulbricht’s online activity
    with DPR’s use of Silk Road. Ulbricht argues that he has a constitutional privacy
    interest in IP address traffic to and from his home and that the government
    obtained the pen/trap orders without a warrant, which would have required
    probable cause.
    B. Corrupt Agents Force and Bridges
    One of the many other tactics that the government used to expose DPR’s
    5
    S.A. refers to the joint sealed appendix in this case. Portions of the sealed
    appendix quoted in this opinion are to that extent unsealed.
    7
    identity was to find low-level Silk Road administrators who helped DPR
    maintain the site, obtain their cooperation, take over their Silk Road usernames,
    and chat with DPR under those identities. The true owners of the administrator
    accounts would assist in the investigation by helping the government chat with
    DPR and access various aspects of the site. Government agents would also create
    their own new usernames and pose as drug dealers or buyers to purchase or sell
    narcotics and occasionally contact DPR directly. One of the government’s
    principal trial witnesses, Special Agent Jared Der-Yeghiayan, used the former
    technique to chat with DPR under the name Cirrus. Cirrus had been a member of
    the Silk Road support staff before the government took over his account, and
    Der-Yeghiayan frequently used Silk Road’s messaging system to communicate
    with DPR and other administrators as Cirrus. Cirrus also gave the government
    access to the staff chat, a separate program allowing DPR to communicate only
    with his employees.
    Two undercover agents involved in the Silk Road investigation are of
    particular import to this appeal: Secret Service Special Agent Shaun Bridges and
    Drug Enforcement Administration (“DEA”) Special Agent Carl Force, both of
    whom were assigned to the Baltimore investigation. Both Force and Bridges used
    8
    their undercover access to exploit the site for their own benefit in various ways,
    and they eventually pleaded guilty to criminal charges in connection with their
    work on the Silk Road investigation.6
    For example, Force and Bridges took over an administrator account
    belonging to Curtis Green, who worked for Silk Road under the name Flush.
    According to the criminal complaint against Force and Bridges, in January 2013,
    Bridges used the Flush username to change other users’ passwords, empty their
    Bitcoin wallets,7 and keep $350,000 in Bitcoins in offshore bank accounts, all while
    attempting to hide his activity through a series of transactions.8 Specifically, the
    6
    Both Force and Bridges pleaded guilty to money laundering and obstruction of
    justice; Force also pleaded guilty to extortion. Force was sentenced to 78 months
    in prison, and Bridges received a 71-month sentence.
    7
    According to the criminal complaint against Ulbricht, a Bitcoin wallet is a
    storage method for Bitcoins. The wallet is associated with a Bitcoin address,
    which is “analogous to the account number for a bank account, while the ‘wallet’
    is analogous to a bank safe where the money in the account is physically stored.”
    App’x 59. Users can transact in Bitcoin by transferring Bitcoins from one “Bitcoin
    address to the Bitcoin address of another user, over the Internet.” 
    Id. Ulbricht does
    not dispute that definition.
    8
    As described below, the government disclosed shortly before trial that Force
    was under investigation for Silk Road corruption, but said nothing about Bridges.
    Specifically, the pretrial disclosure noted that Force was under investigation for
    using the Flush account to steal $350,000, but the criminal complaint against the
    agents alleges that Bridges committed that particular theft. According to the
    government, both Force and Bridges had access to the Flush account, which
    9
    complaint against Force and Bridges alleges that Bridges “act[ed] as an
    administrator to reset pins and passwords on various Silk Road vendors’
    accounts,” then exchanged the Bitcoins for U.S. dollars using the Mt. Gox
    exchanger.9 Supp. App’x 180. Shortly after he committed the January 2013 thefts,
    Bridges asked Force to chat with DPR as Nob, Force’s authorized undercover
    username, to get advice about how to liquidate Bitcoins. He also sought Force’s
    help in convincing Curtis Green (formerly Flush) to help him transfer Bitcoins to
    other accounts, and he ultimately tried to blame Green for the theft.
    With the government’s approval, Force also posed as a drug dealer and
    communicated with DPR as Nob. As part of his official undercover work as Nob,
    Force agreed to sell fraudulent identification documents to DPR for $40,000 in
    Bitcoins. According to the criminal complaint against the agents, Force kept the
    Bitcoins received by his Nob account in connection with that transaction for his
    personal use. On another occasion, again as part of his authorized undercover
    work, Force advised DPR that he had access to information about Silk Road from
    an invented corrupt government employee. DPR paid Force $50,000 in Bitcoins
    might explain their initial suspicion that Force stole the funds.
    9
    Mt. Gox was a prominent Bitcoin exchanger owned by Mark Karpeles.
    10
    for purported inside law enforcement information; Force allegedly purloined that
    payment as well. Moreover, outside his authorized undercover work, Force
    operated another account under the name French Maid, through which he again
    offered to sell DPR information about the government’s Silk Road investigation.
    Acting as French Maid, Force received about $100,000 in Bitcoins that he kept for
    his personal use.
    Force created yet another unauthorized Silk Road account, under the name
    DeathFromAbove, which was unknown to law enforcement until the defense
    identified it during trial. Force used the DeathFromAbove account to try to extort
    money from DPR. For example, in one such chat that took place on April 16,
    2013, DeathFromAbove told DPR that he knew that DPR’s true identity was
    Anand Athavale. DeathFromAbove demanded a payment of $250,000 in
    exchange for which DeathFromAbove would remain silent about DPR’s
    identity.10 There is no evidence that DPR made the requested payment to
    DeathFromAbove; indeed, DPR shrugged off the attempted blackmail as
    10
    DeathFromAbove also referred to the $250,000 payment he demanded as
    “punitive damages.” App’x 875. In the government’s view, the “punitive
    damages” remark referenced the murder of a Silk Road administrator that
    Ulbricht ordered and paid for (but that was never carried out). That and other
    killings that DPR commissioned will be described in more detail below.
    11
    “bogus.”App’x 710.
    As will be explained in more detail below, the district court prevented
    Ulbricht from introducing evidence at trial related to Force’s corruption because
    doing so would have exposed the ongoing grand jury investigation into Force’s
    conduct. The district court also denied Ulbricht discovery related to the
    investigation and excluded certain hearsay statements that arguably revealed
    Force’s corruption. Ulbricht contends on appeal that the district court’s various
    rulings concerning evidence related to Force deprived him of a fair trial.
    Additionally, Ulbricht did not learn of Bridges’s corrupt conduct until after trial
    when the criminal complaint against both agents was unsealed. Thus, in his
    motion for a new trial, he argued that the belated disclosure violated his due
    process rights under Brady v. Maryland, 
    373 U.S. 83
    (1963). Ulbricht contends on
    appeal that the district court incorrectly denied that motion.
    II.   Ulbricht’s Arrest
    Ulbricht was arrested in a San Francisco public library on October 1, 2013,
    after the government had amassed significant evidence identifying him as Dread
    Pirate Roberts. The arrest was successfully orchestrated to catch Ulbricht in the
    act of administering Silk Road as DPR. Federal agents observed Ulbricht enter
    12
    the public library, and a few minutes later Dread Pirate Roberts came online in
    the Silk Road staff chat. Der-Yeghiayan, under the undercover administrator
    username Cirrus, initiated a chat with DPR, asking him to go to a specific place
    on the Silk Road site to address some flagged messages from users. Der-
    Yeghiayan reasoned that this would “force [Ulbricht] to log in under . . . his
    Dread Pirate Roberts account” in the Silk Road marketplace, as well as in the staff
    chat software. Tr. 331-32.
    Once Der-Yeghiayan knew that DPR had logged onto the flagged message
    page in the marketplace, he signaled another agent to effect the arrest. Ulbricht
    was arrested, and incident to that arrest agents seized his laptop. The same chat
    that Der-Yeghiayan had initiated with Dread Pirate Roberts a few minutes earlier
    was open on Ulbricht’s screen. Ulbricht also visited the flagged post in the
    marketplace that Der-Yeghiayan (as Cirrus) had asked DPR to look at during
    their chat. While he was chatting with Cirrus, moreover, Ulbricht had accessed
    Silk Road by using the “Mastermind” page. That page was available only to
    Dread Pirate Roberts.
    A great deal of the evidence against Ulbricht came from the government’s
    search of his laptop and his home after the arrest. On the day of Ulbricht’s arrest,
    13
    the government obtained a warrant to seize Ulbricht’s laptop and search it for a
    wide variety of information related to Silk Road and information that would
    identify Ulbricht as Dread Pirate Roberts. Ulbricht moved to suppress the large
    quantity of evidence obtained from his laptop, challenging the constitutionality
    of that search warrant. Ulbricht argues on appeal that the district court erred in
    denying his motion to suppress. More details concerning the search warrant will
    be described in context below.
    III.   The Trial
    Ulbricht’s trial lasted approximately three weeks, from January 13 through
    February 4, 2015. Judge Forrest handled the complex and contentious trial with
    commendable patience and skill. Although Ulbricht does not challenge the
    sufficiency of the evidence to support the jury’s verdict on any of the counts of
    conviction, we summarize the evidence presented at trial as context for the issues
    raised on appeal.
    A. The Government’s Case
    The government presented overwhelming evidence that Ulbricht created
    Silk Road in 2011 and continued to operate the site throughout its lifetime by
    maintaining its computer infrastructure, interacting with vendors, crafting
    14
    policies for site users, deciding what products would be available for sale on the
    site, and managing a small staff of administrators and software engineers.
    Defense counsel conceded in his opening statement that Ulbricht did in fact
    create Silk Road.
    According to Ulbricht’s own words in a 2009 email, Ulbricht originally
    conceived of Silk Road as “an online storefront that couldn’t be traced back to
    [him] . . . where [his] customers could buy [his] products” and pay for them
    “anonymously and securely.” Tr. 991. From 2009 through 2011, Ulbricht worked
    to get the site up and running, relying on computer programming assistance
    from others, including his friend Richard Bates. According to one of the journal
    entries discovered on his laptop, in 2010 Ulbricht began to grow hallucinogenic
    mushrooms to sell on the site “for cheap to get people interested.” Tr. 899. As the
    site began to garner significant interest in 2011, Ulbricht wrote in his journal that
    he was “creating a year of prosperity and power beyond what I have ever
    experienced before. Silk Road is going to become a phenomenon and at least one
    person will tell me about it, unknowing that I was its creator.” Tr. 899-900.
    1. Evidence Linking Ulbricht to Dread Pirate Roberts
    Around January 2012, the Silk Road user who represented himself as the
    15
    lead administrator of the site adopted the username Dread Pirate Roberts.11 The
    name alludes to the pseudonym of a pirate in the popular novel and film The
    Princess Bride that is periodically passed on from one individual to another.12 In
    order to assure users that posts purporting to be authored by DPR were indeed
    his own, DPR authenticated his posts using an electronic signature known as a
    PGP key.13 Silk Road users had access to a public PGP key, and DPR had a
    private PGP key that he alone could use to sign his Silk Road posts. When DPR
    signed a post using his private key, Silk Road users could run the code in the
    public key, and if the post was signed with the correct private key the user would
    receive a message that the authentication was successful. The government
    recovered DPR’s private PGP key on Ulbricht’s laptop. Importantly, the public
    PGP key did not change during the site’s life span, meaning that DPR used the
    same private key to sign his posts throughout the time that he administered Silk
    Road.
    11
    The timing of this change corresponds to a January 15, 2012 Tor chat between a
    user named “vj” and Ulbricht, in which vj advised Ulbricht to change his
    username from Admin to Dread Pirate Roberts.
    12
    See William Goldman, The Princess Bride: S. Morgenstern’s Classic Tale of True
    Love and High Adventure (1973); The Princess Bride (20th Century Fox 1987).
    13
    PGP stands for “Pretty Good Privacy.”
    16
    Additional evidence supported the conclusion that Ulbricht was Dread
    Pirate Roberts. For example, the instructions that DPR provided to Cirrus (the
    account that Der-Yeghiayan later used for undercover work) for how to access
    the staff chat and contact DPR directly were found in a file on Ulbricht’s laptop.
    The government also discovered the following evidence, covering the entire
    period during which DPR managed the Silk Road site, on Ulbricht’s computer:
    thousands of pages of chat logs with Silk Road employees; detailed journal
    entries describing Ulbricht’s ownership of the site; a list that tracked Ulbricht’s
    tasks and ideas related to Silk Road; a copy of Silk Road’s database; and
    spreadsheets cataloguing both the servers that hosted Silk Road and expenses
    and profits associated with the site. The government seized approximately $18
    million worth of Bitcoins from the wallet on Ulbricht’s laptop and analyzed their
    transaction history (through blockchain records) to determine that about 89% of
    the Bitcoins on Ulbricht’s computer came from Silk Road servers located in
    Iceland.
    A search of Ulbricht’s home yielded additional evidence linking him with
    the site. That evidence included two USB hard drives with versions of documents
    related to Silk Road that were also stored on Ulbricht’s laptop. There were also
    17
    handwritten notes crumpled in Ulbricht’s bedroom trash can about ideas for
    improving Silk Road’s vendor rating system—an initiative that Dread Pirate
    Roberts had just revealed through a post in a discussion forum on the site.
    The government also introduced other circumstantial evidence connecting
    Ulbricht to DPR’s activity on Silk Road, such as evidence matching Ulbricht’s
    actual travel history with DPR’s online discussion of his travel plans. As one
    concrete example, the government discovered a Tor Chat log14 on Ulbricht’s
    laptop memorializing DPR’s chat with a user named H7. On October 30, 2011,
    DPR told H7 that he would be traveling soon. On Ulbricht’s Gmail account,
    which uses an email address that incorporates his full name, the government
    discovered a travel itinerary from CheapAir that indicated that Ulbricht would
    be traveling on November 15, 2011.
    The government introduced several additional examples of DPR
    discussing travel plans that matched up with travel disclosed in Ulbricht’s email
    and social media activity. At one point, for example, Ulbricht uploaded photos to
    his Facebook account in an album entitled “Thailand, February 2012.” DPR
    14
    Tor Chat is a program that allows “communication between people on the Tor
    network.” Tr. 889.
    18
    discussed going to Thailand in a Tor chat on January 27, 2012, indicating that he
    was in “Thailand now,” attracted by the “allure of a warm beach.” Tr. 1300. He
    also mentioned in a January 26 chat with a user named “vj,” which stood for
    Variety Jones, that he was in Thailand to experience the “beaches and jungles.”
    
    Id. at 1298.
    One of the photos in the Thailand Facebook album depicted Ulbricht
    “in front of what appears to be jungles and beaches,” both of which were
    referenced in DPR’s chats from late January. 
    Id. at 1301.
    2. Murders Commissioned by Dread Pirate Roberts
    The government also presented evidence that DPR commissioned the
    murders of five people to protect Silk Road’s anonymity, although there is no
    evidence that any of the murders actually occurred.15 In March 2013, a Silk Road
    15
    Ulbricht was not charged in this case with crimes based on ordering these
    killings, although evidence relating to the murders was introduced at trial as
    actions taken in furtherance of the charged conspiracies and criminal enterprise.
    The killings were referenced again in connection with Ulbricht’s sentencing. He
    faces open attempted murder-for-hire charges in the District of Maryland,
    however. United States v. Ulbricht, No. 13-0222-CCB (D. Md.). That indictment
    charges Ulbricht with the attempted murder of Curtis Green (Flush). According
    to the criminal complaint against the corrupt officers, after Bridges, using Flush’s
    account, stole $350,000 in Bitcoin in January 2013, DPR recruited Nob (Force) to
    kill Flush as punishment for the theft. DPR paid Nob $80,000 to carry out the
    murder, which Force faked to make Ulbricht believe that the task was complete.
    Presumably because the government removed from its trial evidence anything
    that the corrupted agent Force may have touched, it did not present evidence of
    19
    vendor whose username was FriendlyChemist threatened to release “thousands
    of usernames, ordr [sic] amounts, [and] addresses” of Silk Road customers and
    vendors if DPR did not ensure that FriendlyChemist received money from
    another person, Lucydrop. Tr. 1806. Releasing the information would have
    destroyed the affected users’ anonymity, undermining the security of the site. In
    a later chat with another person, RealLucyDrop, DPR wrote that it would be
    “terrible” if the personal information were to be released, and thus he needed
    FriendlyChemist’s “real world identity so I can threaten him with violence if he
    were to release any names.” 
    Id. at 1811.
    The episode escalated from there. DPR connected with Redandwhite, who
    was FriendlyChemist’s supplier, and wrote that “FriendlyChemist is a liability
    and I wouldn’t mind if he was executed.” 
    Id. at 1822.
    After negotiating the
    logistical details of the murder, Ulbricht agreed to pay Redandwhite $150,000 in
    Bitcoins to kill FriendlyChemist. DPR paid Redandwhite, who later confirmed
    that he had received the payment and carried out the murder, and sent what
    appeared to be a photo of the dead victim to DPR. DPR replied that he had
    the Flush murder-for-hire agreement, nor did it rely on that murder at
    sentencing.
    20
    “received the picture and deleted it,” and thanked Redandwhite for his “swift
    action.” 
    Id. at 1892.
    Around the same time, Ulbricht recorded in a file on his
    laptop that he “[g]ot word that the blackmailer was executed.” 
    Id. at 1887.
    The
    government was not able to develop any evidence linking these conversations to
    an actual murder. A reasonable jury could easily conclude, however, that the
    evidence demonstrated that Ulbricht ordered and paid for the killing, and that he
    believed that it had occurred.
    Later, DPR ordered four other murders through Redandwhite. Dread
    Pirate Roberts identified another Silk Road user, Tony76, who knew
    FriendlyChemist and might compromise the site’s anonymity. After some
    negotiations, DPR agreed to pay Redandwhite $500,000 in Bitcoins to kill Tony76
    and three of his associates. DPR then sent the payment to Redandwhite. On April
    6, 2013, Ulbricht wrote in a file on his laptop that he “[g]ave angels go ahead to
    find tony76.” Tr. 1900. Two days later, Ulbricht recorded that he “[s]ent payment
    to angels for hit on tony76 and his three associates.” 
    Id. One of
    the government’s
    expert witnesses was able to link the payments for all five murders to Bitcoin
    wallets located on Ulbricht’s laptop. Again, while the evidence demonstrates that
    Ulbricht ordered and paid substantial sums for the murders, there is no evidence
    21
    that the killings actually took place; the government theorized that Redandwhite
    had tricked Ulbricht into thinking that he actually committed the murders, but
    that in fact he had not.
    B. The Defense Case
    As noted above, Ulbricht conceded at trial that he had created Silk Road,
    and he was caught red-handed operating the site at the end of the investigation.
    His principal defense strategy at trial—more of an effort at mitigation than
    outright denial of his guilt of the conspiracy and other charges in the
    indictment—was to admit his role at the beginning and end of the site’s
    operation, but to contend that he sold Silk Road to someone else in 2011 and
    abandoned his role as its administrator, only to be lured back by the successor
    DPR near the end of its operation to take the blame for operating the site. The
    defense attempted on several occasions to implicate as alternative suspects
    Karpeles and Athavale, both of whom the government had investigated for a
    possible connection to Silk Road but later abandoned as candidates for DPR’s
    real-world identity. As part of his alternative-perpetrator defense, Ulbricht
    theorized that the person or persons who operated as the true Dread Pirate
    Roberts during the purported interim period planted incriminating evidence on
    22
    his laptop in order to frame him. For the most part, the defense advanced this
    theory through cross-examination of government witnesses. Ulbricht did not
    testify at trial.
    One point in the testimony of Richard Bates exemplifies the defense’s
    approach and the government’s response. Bates, Ulbricht’s friend who assisted
    with computer programming issues when Ulbricht launched Silk Road, testified
    for the government. According to Bates, Ulbricht told him in November 2011 that
    he had sold Silk Road to someone else, a claim that Bates believed at the time to
    be true. Moreover, in a February 2013 Google chat between Bates and Ulbricht,
    Ulbricht wrote that he was “[g]lad” that Silk Road was “not [his] problem
    anymore.” Tr. 1140-41.16 Bates understood that to mean that Ulbricht no longer
    worked on the site.
    To mitigate any damage from Bates’s testimony, the government
    introduced a December 9, 2011 Tor chat between Ulbricht and vj. In that chat, vj
    asked Ulbricht whether anyone else knew about his involvement in Silk Road.
    16
    There are two versions of the trial transcript for January 22, 2015 on the district
    court docket. The page citations here refer to the version of the transcript marked
    “corrected,” which is listed on the district court docket as Document No. 208 (14-
    cr-68).
    23
    Ulbricht responded: “[U]nfortunately yes. There are two, but they think I sold the
    site and got out and they are quite convinced of it.” Tr. 1191. He further wrote
    that those two people thought he sold the site “about a month ago,” 
    id., which roughly
    corresponds to the November 2011 conversation between Bates and
    Ulbricht. Significantly, it was shortly after this conversation that vj suggested that
    Ulbricht change his online identity to DPR. In view of the fictional character it
    referenced, the government contended that the online moniker DPR was
    deliberately adopted to support the cover story that the lead administrator of Silk
    Road changed over time.
    Thus, although the government elicited testimony that Ulbricht told Bates
    that he sold the site in 2011, it also presented evidence that Ulbricht had lied to
    Bates about that sale and continued to operate the site in secret.
    1. Cross-Examination of Government Witnesses
    Ulbricht’s defense depended heavily on cross-examination of government
    witnesses, much of which was designed to support the argument that either
    Karpeles or Athavale was the real DPR, or that multiple people operated as
    Dread Pirate Roberts during Silk Road’s life span. The district court limited his
    cross-examination in two ways that Ulbricht challenges on appeal. First, the
    24
    district court prevented Ulbricht from exploring several specific topics with Der-
    Yeghiayan, the government’s first witness, through whom it introduced much of
    its evidence. Those topics included, inter alia, Der-Yeghiayan’s prior suspicions
    that Karpeles was DPR. Second, the district court limited Ulbricht’s ability to
    cross examine FBI computer scientist Thomas Kiernan, who testified about
    evidence that he discovered on Ulbricht’s laptop, concerning several specific
    technical issues related to software on Ulbricht’s computer. More details about
    those attempted cross-examinations will be discussed in context below.
    2. Hearsay Statements
    Ulbricht also attempted to introduce two hearsay statements in his defense,
    both of which the district court excluded as inadmissible. Those hearsay
    statements comprise: (1) chats between DPR and DeathFromAbove (Force)
    concerning Force’s attempt to extort money from DPR in exchange for
    information about the government’s investigation of Silk Road; and (2) the
    government’s letter describing a statement by Andrew Jones, a site administrator,
    concerning one particular conversation that he had with DPR. The contents of
    those hearsay statements and other relevant facts will be discussed in more detail
    below.
    25
    3. Defense Expert Witnesses
    Long after the trial began on January 13, 2015, and shortly before the
    government rested on February 2 and the defense rested on February 3, Ulbricht
    disclosed to the government his intent to call two expert witnesses: Dr. Steven
    Bellovin and Andreas Antonopoulos.17 The Antonopoulos disclosure indicated
    that he would testify on several subjects relevant to Silk Road, including “the
    origins of Bitcoin,” “the various purposes and uses of Bitcoin,” “the mechanics of
    Bitcoin transactions,” “the value of Bitcoin over time since its inception,” and
    “the concepts of Bitcoin speculating and Bitcoin mining,” among other things.
    App’x 349. The Bellovin disclosure followed a similar pattern, indicating that he
    would testify about “[g]eneral principles of internet security and vulnerabilities,”
    the “import of some lines of PHP code provided to defense counsel in
    discovery,” and “[g]eneral principles of public-key cryptography,” among other
    topics. 
    Id. at 360.
    Neither disclosure summarized the opinions that the experts
    would offer on those subjects, nor did either identify the bases for the experts’
    opinions.
    17
    Ulbricht noticed his intent to call Antonopoulos on January 26 and Bellovin on
    January 30, 2015.
    26
    On January 29 and 31, the government moved to preclude the testimony of
    both proffered experts. The government argued that the expert notices were
    untimely and did not contain the information required by Rule 16 of the Federal
    Rules of Criminal Procedure, including a summary of the opinions that the
    experts would offer on the stand.18 On February 1—three days before the end of
    the trial—the district court granted the government’s motions and precluded
    both experts from testifying, concluding that the defendant’s notices were late
    and that the disclosures were substantively inadequate under Rule 16. Ulbricht
    claims that the district court erred in precluding his experts from testifying.
    In sum, the defense case was limited to cross-examining government
    witnesses, briefly calling four character witnesses, having a defense investigator
    authenticate a task list on Ulbricht’s computer, and reading a few of DPR’s posts
    into the record. Ulbricht contends, however, that his defense was hamstrung by
    the rulings described above.
    18
    The government also argued generally that some of the topics identified in the
    disclosures were not relevant to Ulbricht’s case or did not require expert
    testimony.
    27
    C. The Verdict and Post-Trial Motion
    After deliberating for about three and a half hours, the jury returned a
    guilty verdict on all seven counts in the Indictment. As described in more detail
    below, Ulbricht then moved for a new trial under Rule 33, Fed. R. Crim. P. The
    district court denied the motion, and Ulbricht argues here that it erred in doing
    so.
    IV.   Sentencing
    The United States Probation Office prepared the Pre-Sentence Investigation
    Report (“PSR”) in March 2015. It described the offense conduct in detail and
    discussed the five murders that Ulbricht allegedly hired Redandwhite to
    commit.19 Over Ulbricht’s objection, the PSR also discussed six drug-related
    deaths that the government contended, and the district court found, were
    connected with Silk Road. Circumstantial evidence linked each of those fatalities
    with varying degrees of certainty to the decedent’s purchase of drugs on Silk
    Road. For example, one user died from an overdose of heroin combined with
    other drugs. The deceased individual was found with a needle and a bag of
    19
    The PSR did not refer to the additional murder of “Flush” that DPR allegedly
    paid Force, under his undercover identity Nob, to commit. See supra note 15.
    28
    heroin, as well as a torn-open delivery package. Open on his computer was a Silk
    Road chat in which a vendor described the package of heroin that was due to
    arrive that day, including a tracking number that matched the opened package.
    Two other individuals whose deaths the PSR described were Silk Road
    customers who purchased drugs on the site shortly before their deaths. A fourth
    person died after ingesting a synthetic drug originally purchased on Silk Road
    that he obtained through an intermediary dealer, and a fifth died after leaping
    from a balcony while high on a psychedelic drug that he bought from the site. A
    sixth person died of pneumonia after placing over thirty orders for heroin and
    other drugs on Silk Road; the autopsy report theorized that his drug use may
    have “blunted the deceased’s perception of the severity of his illness,” thus
    contributing to his premature death. PSR ¶ 83. In arguing that the district court
    should consider the six deaths, the government explained that they “illustrate the
    obvious: that drugs can cause serious harm, including death.” App’x 902.
    In the first of several sentencing submissions, Ulbricht urged the district
    court not to consider the six drug-related deaths and to strike them from the PSR.
    In support of that argument, Ulbricht claimed that Silk Road had harm-reducing
    effects, meaning that it made drug use less dangerous. Specifically, Ulbricht
    29
    employed Dr. Fernando Caudevilla (username Doctor X), a physician who
    provided drug-use advice to the site’s customers. Caudevilla spent up to two or
    three hours a day on Silk Road discussion fora and sent over 450 messages
    providing guidance about illegal drug dosage and administration, as well as
    information about the harms associated with certain drugs. Caudevilla also
    provided weekly reports to DPR concerning the advice he gave to the site’s users.
    Ulbricht further claimed that Silk Road allowed for better drug quality control
    because vendors were subject to a rating system,20 buyers were able to choose
    from among many different sellers, and the site’s anonymity encouraged free
    dialogue about drug use that helped mitigate the stigma accompanying drug
    addiction.21 According to Caudevilla, when the site received negative feedback
    about the quality of the drugs sold by a vendor, that vendor was removed from
    20
    As the government pointed out in its sentencing submission, fake vendor
    reviews were commonplace, and vendors sometimes coerced customers into
    giving them perfect ratings.
    21
    Ulbricht referenced a study by Tim Bingham, who researched Silk Road users
    between September 2012 and August 2013. Bingham interviewed Silk Road
    customers and concluded that the site operated as a “novel technological drug
    subculture, potentially minimiz[ing] drug-related stigma by reinforcing a[] sense
    of community.” App’x 905. Thus, Bingham concluded, and Ulbricht argued, that
    Silk Road encouraged more “responsible forms of recreational drug use.” 
    Id. at 906.
    30
    the site. Finally, Ulbricht claimed that the site reduced violence associated with
    the drug trade by providing a safe, computer-based method of purchasing drugs.
    Ulbricht also submitted an expert report from Dr. Mark Taff, which
    provided an alternative reason for excluding the six deaths from the PSR. In his
    report, Dr. Taff explained that, based on the information available, it was
    impossible to know with medical certainty that Silk Road drugs caused the six
    deaths described in the PSR. There were “gaping holes” in the investigations into
    each death, and some were missing autopsy reports, toxicology reports, and
    death certificates. App’x 911. Moreover, Dr. Taff claimed that it was impossible to
    know the cause of each death because several of the deceased had ingested
    multiple drugs prior to their deaths. Ulbricht argued that, absent a clear causal
    link between the deaths and the offense conduct, the deaths were not relevant to
    his sentencing at all.
    The defense later submitted another sentencing memorandum, which
    included 97 letters from friends and family describing Ulbricht’s good character
    as well as academic articles about the myriad problems associated with unduly
    severe sentences for drug crimes. He also urged the district court not to consider
    the five murders commissioned by DPR, in part because he claimed only to have
    31
    fantasized about the murders, implying that he did not expect them to be carried
    out. In its sentencing submission, the government requested that the district
    court impose a sentence substantially above the twenty-year mandatory
    minimum.
    Ulbricht’s sentencing hearing took place on May 29, 2015.22 The district
    court concluded that Ulbricht’s offense level was 43—the highest possible offense
    level under the Sentencing Guidelines—and that his criminal history category
    was I.23 The high offense level largely resulted from the massive quantity of
    drugs trafficked using Silk Road, as well as several enhancements, including one
    for directing the use of violence, U.S.S.G. § 2D1.1(b)(2).24 Ulbricht does not
    dispute that calculation. Due to the high offense level, the Guidelines advisory
    22
    At sentencing, the district court vacated Ulbricht’s convictions on Counts One
    and Three because they were lesser included offenses of Counts Two and Four
    respectively. Ulbricht was therefore sentenced on Counts Two, Four, Five, Six,
    and Seven. The district court based its Guidelines calculation only on those
    counts.
    23
    The calculated offense level was actually 50, which is higher than the maximum
    offense level of 43 on the Guidelines sentencing table. The Guidelines provide
    that “[a]n offense level of more than 43 is to be treated as an offense level of 43.”
    U.S.S.G. ch. 5 pt. A, cmt. n.2.
    24
    Because of the grouping rules, U.S.S.G. ch. 3 pt. D, the lower offense levels of
    the computer hacking and fraudulent identification charges did not contribute to
    Ulbricht’s offense level.
    32
    sentence “range” was life in prison, and the U.S. Probation Office recommended
    that sentence.
    At the sentencing hearing, the district court resolved several disputed
    issues of fact. For example, because Ulbricht contested his responsibility for the
    five commissioned murders for hire, the district court found by a preponderance
    of the evidence that Ulbricht did in fact commission the murders, believing that
    they would be carried out. The district court characterized the evidence of the
    murders for hire, which included Ulbricht’s journal, chats with other Silk Road
    users, and the evidence showing that Ulbricht actually paid a total of $650,000 in
    Bitcoins for the killings, as “ample and unambiguous.” App’x 1465.
    The court then turned to the six drug-related deaths described in the PSR.
    Over Ulbricht’s objection, the district court found that the deaths were “related
    conduct relevant to his sentencing” because the “question as to whether this
    information is properly included in the PSR is whether the Court finds, by a
    preponderance of the evidence[,] that the deaths, in some way, related to Silk
    Road.” 
    Id. at 1472.
    It went on to explain that “the relevant offense committed is
    the unlawful distribution of drugs and the running of a criminal drug enterprise,
    . . . [and] based on the evidence before the Court, the sale of the drugs through
    33
    Silk Road caused harm to the decedents.” 
    Id. at 1473.
    The district court described
    the facts associated with five of the deaths and specifically found that each was
    connected to Silk Road, rejecting the defendant’s argument that but-for causation
    was required in order for the court to consider the deaths as relevant to the
    offense conduct.25 Parents of two of the decedents also made statements at the
    proceeding, describing the emotional impact that the losses had on them and
    their families.
    In the course of explaining its reasons for choosing Ulbricht’s sentence, the
    district court discussed the facts of Ulbricht’s offense, his apparent character, and
    the purposes of criminal punishment. The court described Doctor X as
    “enabling,” App’x 1530, rather than reducing the harms associated with drug
    use, emphasized the social costs attendant to expanding the scope of the drug
    market, discussed the five murders for hire, and stated that the sentence imposed
    on Ulbricht could have a powerful general deterrent effect because the case had
    25
    The district court did not specifically address one of the six deaths. That
    decedent was a frequent Silk Road customer who was found dead in his home
    with a used syringe and other drug paraphernalia. The record does not indicate
    why the district court did not discuss that case, and neither party makes any
    argument based on that omission.
    34
    attracted an unusually large amount of publicity. The court then sentenced
    Ulbricht principally to life imprisonment.
    This appeal followed.
    DISCUSSION
    On appeal, Ulbricht raises a number of claims of error. For purposes of
    organizational clarity, we group them into three categories, and present them in
    the order in which the issues arose in the district court. Accordingly, we discuss
    first Ulbricht’s claims that much of the evidence against him should have been
    suppressed because it was obtained in violation of his Fourth Amendment rights;
    second, his arguments that the district court’s evidentiary errors denied him a
    fair trial; and third, his objections to his sentence.
    I.    Fourth Amendment Issues
    Ulbricht claims that the district court erred in denying his motion to
    suppress evidence obtained in violation of the Fourth Amendment. On appeal
    from a denial of a suppression motion, “we review a district court’s findings of
    fact for clear error, and its resolution of questions of law and mixed questions of
    law and fact de novo.” United States v. Bohannon, 
    824 F.3d 242
    , 247-48 (2d Cir.
    2016). Ulbricht raises two principal arguments. First, he contends that the
    35
    pen/trap orders that the government used to monitor IP address traffic to and
    from his home router violated the Fourth Amendment because the government
    obtained the orders without a warrant. Second, he claims that the warrants
    authorizing the government to search his laptop as well as his Google and
    Facebook accounts violated the Fourth Amendment’s particularity requirement.
    We reject those contentions and affirm the denial of Ulbricht’s motion to
    suppress.
    A. Pen/Trap Orders
    Pursuant to orders issued by United States magistrate judges in the
    Southern District of New York, the government used five pen registers and trap
    and trace devices to monitor IP addresses associated with Internet traffic to and
    from Ulbricht’s wireless home router and devices that regularly connected to that
    router. The government obtained the orders pursuant to the Pen/Trap Act, which
    provides that a government attorney “may make [an] application for an order . . .
    authorizing or approving the installation and use of a pen register or a trap and
    trace device . . . to a court of competent jurisdiction.” 18 U.S.C. § 3122(a)(1). A
    “pen register” is defined as a “device or process which records or decodes
    dialing, routing, addressing, or signaling information transmitted by an
    36
    instrument or facility from which a wire or electronic communication is
    transmitted,” and “shall not include the contents of any communication.” 
    Id. § 3127(3).
    A “trap and trace” device means “a device or process which captures
    the incoming electronic or other impulses which identify the originating number
    or other dialing, routing, addressing, and signaling information reasonably likely
    to identify the source of a wire or electronic communication.” 
    Id. § 3127(4).
    Like
    pen registers, trap and trace devices may not capture the “contents of any
    communication.” 
    Id. The statute
    does not require a search warrant for the use of a
    pen register or trap and trace device, nor does it demand the kind of showing
    required to obtain such a warrant. Rather, the statute requires only that the
    application contain a “certification . . . that the information likely to be obtained is
    relevant to an ongoing criminal investigation.” 
    Id. § 3122(b)(2).
    The orders in this case authorized the government to “use a pen register
    and trap and trace device to identify the source and destination [IP] addresses,
    along with the dates, times, durations, ports of transmission, and any
    Transmission Control Protocol (‘TCP’) connection data,26 associated with any
    26
    Data are transmitted on the Internet via discrete packets, rather than in a
    continuous stream. TCP is a “communications protocol used to process such data
    packets associated with popular Internet applications,” such as browser and e-
    37
    electronic communications sent to or from” various devices, including Ulbricht’s
    home wireless router and his laptop.27 S.A. 93. In each order, the government
    specified that it did not seek to obtain the contents of any communications.
    Instead, it sought authorization to collect only “dialing, routing, addressing, and
    signaling information” that was akin to data captured by “traditional telephonic
    pen registers and trap and trace devices.” 
    Id. at 130.
    Ulbricht claims that the
    pen/trap orders violated the Fourth Amendment because he had a reasonable
    expectation of privacy in the IP address routing information that the orders
    allowed the government to collect.28
    mail applications. S.A. 97. Like IP address data, the TCP data that the orders
    permitted the government to acquire do not include the contents of
    communications, and Ulbricht has not expressed any independent concern over
    the government’s collection of TCP connection data.
    27
    Some of the pen/trap orders phrased the scope of the order slightly differently.
    For example, one order authorized installing “a trap and trace device to identify
    the source [IP] address of any Internet communications directed to, and a pen
    register to determine the destination IP addresses of any Internet
    communications originating from,” the relevant devices. S.A. 67. In other words,
    not every order sought TCP connection data as well as IP address information.
    Neither party has suggested that the differences among the pen/trap orders are
    material to any issue presented by this appeal.
    28
    In the district court, Ulbricht made the same arguments concerning his Fourth
    Amendment privacy interest in the information captured by the pen registers
    and trap and trace devices. The district court ruled generally that the “type of
    information sought [in the orders] was entirely appropriate for that type of
    38
    The Fourth Amendment to the United States Constitution provides that:
    “The right of the people to be secure in their persons, houses, papers, and effects,
    against unreasonable searches and seizures, shall not be violated, and no
    Warrants shall issue, but upon probable cause, supported by Oath or affirmation,
    and particularly describing the place to be searched, and the persons or things to
    be seized.” The “cornerstone of the modern law of searches is the principle that,
    to mount a successful Fourth Amendment challenge, a defendant must
    demonstrate that he personally has an expectation of privacy in the place
    searched.” United States v. Haqq, 
    278 F.3d 44
    , 47 (2d Cir. 2002) (internal quotation
    marks omitted). Thus, a “Fourth Amendment ‘search[]’ . . . does not occur unless
    the search invades an object or area [in which] one has a subjective expectation of
    privacy that society is prepared to accept as objectively reasonable.” United States
    v. Hayes, 
    551 F.3d 138
    , 143 (2d Cir. 2008).
    The Supreme Court has long held that a “person has no legitimate
    expectation of privacy in information he voluntarily turns over to third parties,”
    order.” App’x 208. The court declined to address Ulbricht’s “novel Fourth
    Amendment arguments” regarding the pen/trap devices because he had “not
    established the requisite privacy interest . . . to” demonstrate his standing to
    challenge the orders. 
    Id. The government
    has agreed that Ulbricht has standing to
    pursue his Fourth Amendment arguments on appeal.
    39
    including phone numbers dialed in making a telephone call and captured by a
    pen register. Smith v. Maryland, 
    442 U.S. 735
    , 743-44 (1979). This is so because
    phone users “typically know that they must convey numerical information to the
    phone company; that the phone company has facilities for recording this
    information; and that the phone company does in fact record this information for
    a variety of legitimate business purposes.” 
    Id. at 743.
    Similarly, “e-mail and
    Internet users . . . rely on third-party equipment in order to engage in
    communication.” United States v. Forrester, 
    512 F.3d 500
    , 510 (9th Cir. 2008).
    Internet users thus “should know that this information is provided to and used
    by Internet service providers for the specific purpose of directing the routing of
    information.” 
    Id. Moreover, “IP
    addresses are not merely passively conveyed
    through third party equipment, but rather are voluntarily turned over in order to
    direct the third party’s servers.” United States v. Christie, 
    624 F.3d 558
    , 574 (3d Cir.
    2010) (internal quotation marks omitted).
    Ulbricht notes that questions have been raised about whether some aspects
    of modern technology, which entrust great quantities of significant personal
    information to third party vendors, arguably making extensive government
    surveillance possible, call for a re-evaluation of the third-party disclosure
    40
    doctrine established by Smith. See, e.g., United States v. Jones, 
    565 U.S. 400
    , 417-18
    (2012) (Sotomayor, J., concurring); American Civil Liberties Union v. Clapper, 
    785 F.3d 787
    , 824 (2d Cir. 2015). We remain bound, however, by that rule until and
    unless it is overruled by the Supreme Court. See United States v. Gomez, 
    580 F.3d 94
    , 104 (2d Cir. 2009); see also United States v. Wheelock, 
    772 F.3d 825
    , 829 (8th Cir.
    2014).
    Moreover, whatever novel or more intrusive surveillance techniques might
    present future questions concerning the appropriate scope of the third-party
    disclosure doctrine, the orders in this case do not present such issues. The
    recording of IP address information and similar routing data, which reveal the
    existence of connections between communications devices without disclosing the
    content of the communications, are precisely analogous to the capture of
    telephone numbers at issue in Smith. That is why the orders here fit comfortably
    within the language of a statute drafted with the earlier technology in mind. The
    substitution of electronic methods of communication for telephone calls does not
    alone create a reasonable expectation of privacy in the identities of devices with
    whom one communicates. Nor does it raise novel issues distinct from those long
    since resolved in the context of telephone communication, with which society has
    41
    lived for the nearly forty years since Smith was decided. Like telephone
    companies, Internet service providers require that identifying information be
    disclosed in order to make communication among electronic devices possible. In
    light of the Smith rule, no reasonable person could maintain a privacy interest in
    that sort of information.
    We therefore join the other circuits that have considered this narrow
    question and hold that collecting IP address information devoid of content is
    “constitutionally indistinguishable from the use of a pen register.” 
    Forrester, 512 F.3d at 510
    ; see, e.g., 
    Wheelock, 772 F.3d at 828
    (holding that the defendant “cannot
    claim a reasonable expectation of privacy in [the] government’s acquisition of his
    subscriber information, including his IP address and name,” because it had been
    “revealed to a third party” (internal quotation marks omitted)); 
    Christie, 624 F.3d at 573
    (holding that there is no expectation of privacy in “subscriber information
    provided to an internet provider,” such as an IP address (internal quotation
    marks omitted)); see also Guest v. Leis, 
    255 F.3d 325
    , 336 (6th Cir. 2001) (holding
    that “computer users do not have a legitimate expectation of privacy in their
    [bulletin board] subscriber information because they have conveyed it to another
    person”); United States v. Graham, 
    824 F.3d 421
    , 432 (4th Cir. 2016) (en banc)
    42
    (noting that “third-party information relating to the sending and routing of
    electronic communications does not receive Fourth Amendment protection”);
    United States v. Carpenter, 
    819 F.3d 880
    , 887 (6th Cir. 2016) (“[C]ourts have not
    (yet, at least) extended [Fourth Amendment] protections to the internet analogue
    to envelope markings, namely the metadata used to route internet
    communications, like . . . IP addresses.”). Where, as here, the government did not
    access the contents of any of Ulbricht’s communications, it did not need to obtain
    a warrant to collect IP address routing information in which Ulbricht did not
    have a legitimate privacy interest. We therefore reject Ulbricht’s contention that
    the issuance of such orders violated his Fourth Amendment rights.29
    29
    The issue presented in this case is narrowly confined to orders that are limited
    to the capture of IP addresses, TCP connection data, and similar routing
    information. Our holding therefore does not address other, more invasive
    surveillance techniques that capture more information (such as content), which
    may require a warrant issued on probable cause or an order pursuant to Title III
    of the Omnibus Crime Control and Safe Streets Act of 1968, codified as amended
    at 18 U.S.C. §§ 2510-22. See generally In the Matter of a Warrant for All Content &
    Other Info. Associated with the Email Account xxxxxxx@gmail.com Maintained at
    Premises Controlled by Google, Inc., 
    33 F. Supp. 3d 386
    , 393-96 (S.D.N.Y. 2014), as
    amended (Aug. 7, 2014) (describing the available caselaw concerning search
    warrants of email accounts). Similarly, to the extent that some of the out-of-circuit
    cases cited in the text also address the Fourth Amendment status of other types
    of evidence, such as historical cell-site location information, we express no views
    on such issues, which are not presented in this case.
    43
    Ulbricht’s additional arguments are not persuasive. Ulbricht contends
    generally that pen/trap orders may monitor a communication’s content by
    tracking metadata, but he does not identify what metadata the government might
    have collected or explain how the pen/trap orders in this case gave the
    government information concerning the content of his communications. He also
    claims that the orders violated the Fourth Amendment by impermissibly
    monitoring activity within his home, relying on Kyllo v. United States, 
    533 U.S. 27
    (2001). In Kyllo, the Court held that using thermal-imaging technology from
    outside the home to discern whether a person was growing marijuana in the
    home might reveal innocent, non-criminal information in which a resident has a
    privacy interest. 
    Id. at 38.
    Ulbricht contends that monitoring IP address traffic
    through his router is similar to the thermal-imaging technology because it might
    reveal when and how Ulbricht used his computer when he was at home. The
    same can be said, however, of an ordinary telephone pen register, which can
    reveal if, when, and how a person uses his or her home phone to make calls. See
    
    Smith, 442 U.S. at 743
    . IP address traffic similarly reveals whether an Internet
    subscriber (or, more precisely, a person who uses the subscriber’s Internet
    connection) is home and using the Internet. Nothing in Kyllo suggests that
    44
    government monitoring of data disclosed to an outside telephone or Internet
    provider for ordinary business purposes becomes constitutionally suspect when
    investigators use that information to draw inferences about whether someone is
    making telephone calls or accessing websites from inside his or her home. We
    therefore see no constitutional difference between monitoring home phone
    dialing information and IP address routing data. Thus, we conclude that the pen
    register and trap and trace orders did not violate the Fourth Amendment.30
    B. Search Warrants
    Ulbricht also contends that the warrants authorizing the search and seizure
    of his laptop as well as his Facebook and Google accounts violated the Fourth
    30
    Ulbricht’s alternative argument, that the pen/trap orders violated the Pen/Trap
    Act and the Stored Communications Act (“SCA”) because they sought
    prospective data, is without merit. Ulbricht claims that the orders were obtained
    both through the Pen/Trap Act, 18 U.S.C. §§ 3121-27, and the SCA, 18 U.S.C.
    § 2703(d). To the contrary, each pen/trap order (and the underlying requests for
    such orders) relied exclusively on the Pen/Trap Act, not the SCA. The fact that
    one of the government’s goals was to monitor IP address traffic to match
    Ulbricht’s Internet activity with DPR’s does not undermine the validity of the
    orders. The orders themselves did not allow the government to track the location
    of the router and other equipment to which the trap and trace device was
    attached. Thus, they were not “geo-locating” devices, as Ulbricht suggests, any
    more than subpoenas for hotel registers, parking tickets, and credit card receipts,
    or any other methods by which the government obtains information that can be
    used to identify a suspect’s location at particular points in time.
    45
    Amendment’s particularity requirement. The Fourth Amendment explicitly
    commands that warrants must be based on probable cause and must
    “particularly describ[e] the place to be searched, and the persons or things to be
    seized.” U.S. Const. amend. IV. “It is familiar history that indiscriminate searches
    and seizures conducted under the authority of ‘general warrants’ were the
    immediate evils that motivated the framing and adoption of the Fourth
    Amendment.” Payton v. New York, 
    445 U.S. 573
    , 583 (1980). Those general
    warrants “specified only an offense,” leaving “to the discretion of the executing
    officials the decision as to which persons should be arrested and which places
    should be searched.” Steagald v. United States, 
    451 U.S. 204
    , 220 (1981). The
    principal defect in such a warrant was that it permitted a “general, exploratory
    rummaging in a person’s belongings,” Andresen v. Maryland, 
    427 U.S. 463
    , 480
    (1976) (internal quotation marks omitted), a problem that the Fourth Amendment
    attempted to resolve by requiring the warrant to “set out with particularity” the
    “scope of the authorized search,” Kentucky v. King, 
    563 U.S. 452
    , 459 (2011).31
    31
    In addition to preventing general searches, the particularity requirement serves
    two other purposes not relevant to this appeal: “preventing the seizure of objects
    upon the mistaken assumption that they fall within the magistrate’s
    authorization, and preventing the issuance of warrants without a substantial
    factual basis.” United States v. Young, 
    745 F.2d 733
    , 759 (2d Cir. 1984).
    46
    To be sufficiently particular under the Fourth Amendment, a warrant must
    satisfy three requirements. First, “a warrant must identify the specific offense for
    which the police have established probable cause.” United States v. Galpin, 
    720 F.3d 436
    , 445 (2d Cir. 2013). Second, “a warrant must describe the place to be
    searched.” 
    Id. at 445-46.
    Finally, the “warrant must specify the items to be seized
    by their relation to designated crimes.” 
    Id. at 446
    (internal quotation marks
    omitted).
    “Where, as here, the property to be searched is a computer hard drive, the
    particularity requirement assumes even greater importance.” 
    Id. A general
    search
    of electronic data is an especially potent threat to privacy because hard drives
    and e-mail accounts may be “akin to a residence in terms of the scope and
    quantity of private information [they] may contain.” 
    Id. The “seizure
    of a
    computer hard drive, and its subsequent retention by the government, can
    [therefore] give the government possession of a vast trove of personal
    information about the person to whom the drive belongs, much of which may be
    entirely irrelevant to the criminal investigation that led to the seizure.” United
    States v. Ganias, 
    824 F.3d 199
    , 217 (2d Cir. 2016) (en banc). Such sensitive records
    might include “[t]ax records, diaries, personal photographs, electronic books,
    47
    electronic media, medical data, records of internet searches, [and] banking and
    shopping information.” 
    Id. at 218.
    Because of the nature of digital storage, it is not
    always feasible to “extract and segregate responsive data from non-responsive
    data,” 
    id. at 213,
    creating a “serious risk that every warrant for electronic
    information will become, in effect, a general warrant,” 
    Galpin, 720 F.3d at 447
    (internal quotation marks omitted). Thus, we have held that warrants that fail to
    “link [the evidence sought] to the criminal activity supported by probable cause”
    do not satisfy the particularity requirement because they “lack[] meaningful
    parameters on an otherwise limitless search” of a defendant’s electronic media.
    United States v. Rosa, 
    626 F.3d 56
    , 62 (2d Cir. 2010).
    The Fourth Amendment does not require a perfect description of the data
    to be searched and seized, however. Search warrants covering digital data may
    contain “some ambiguity . . . so long as law enforcement agents have done the
    best that could reasonably be expected under the circumstances, have acquired
    all the descriptive facts which a reasonable investigation could be expected to
    cover, and have insured that all those facts were included in the warrant.” 
    Galpin, 720 F.3d at 446
    (internal quotation marks omitted).
    48
    Moreover, it is important to bear in mind that a search warrant does not
    necessarily lack particularity simply because it is broad. Since a search of a
    computer is “akin to [a search of] a residence,” 
    id., searches of
    computers may
    sometimes need to be as broad as searches of residences pursuant to warrants.
    Similarly, traditional searches for paper records, like searches for electronic
    records, have always entailed the exposure of records that are not the objects of
    the search to at least superficial examination in order to identify and seize those
    records that are. And in many cases, the volume of records properly subject to
    seizure because of their evidentiary value may be vast. None of these
    consequences necessarily turns a search warrant into a prohibited general
    warrant.
    1. Laptop Search Warrant
    The warrant authorizing the search and seizure of Ulbricht’s laptop (the
    “Laptop Warrant”) explicitly incorporated by reference an affidavit listing the
    crimes charged, which at the time included narcotics trafficking, computer
    hacking, money laundering, and murder-for-hire offenses in violation of 21
    U.S.C. § 846, 18 U.S.C. §§ 1030, 1956, and 1958. See In re 650 Fifth Ave. & Related
    Properties, 
    830 F.3d 66
    , 101 (2d Cir. 2016) (describing the requirements for a
    49
    criminal search warrant’s incorporation of an affidavit by reference).32 The
    affidavit also described the workings of Silk Road and the role of Dread Pirate
    Roberts in operating the site and included a wealth of information supporting a
    finding that there was probable cause to believe that Ulbricht and DPR were the
    same person. Based on that information, the Laptop Warrant alleged that
    Ulbricht “use[d] [the laptop] in connection with his operation of Silk Road,” and
    that there was “probable cause to believe that evidence, fruits, and
    instrumentalities of the [charged offenses]” would be found on the laptop. S.A.
    246.33
    Generally speaking, the Laptop Warrant divided the information to be
    searched for and seized into two categories. The first covered evidence
    concerning Silk Road that was located on the computer, including, inter alia,
    “data associated with the Silk Road website, such as web content, server code, or
    database records”; any evidence concerning servers or computer equipment
    connected with Silk Road; e-mails, private messages, and forum postings or
    32
    Because the warrant incorporated the affidavit by reference, we refer to the
    documents together as the Laptop Warrant for the sake of simplicity.
    33
    Ulbricht does not challenge the existence of probable cause to believe both that
    he committed these offenses and that the laptop would contain evidence of them.
    50
    “other communications concerning Silk Road in any way”; evidence concerning
    “funds used to facilitate or proceeds derived from Silk Road,” including Bitcoin
    wallet files and transactions with Bitcoin exchangers, or “information concerning
    any financial accounts . . . where Silk Road funds may be stored”; and “any
    evidence concerning any illegal activity associated with Silk Road.” 
    Id. at 246-48.
    The second category of information in the Laptop Warrant included
    “evidence relevant to corroborating the identification of Ulbricht as the Silk Road
    user ‘Dread Pirate Roberts.’” 
    Id. at 248.
    In order to connect Ulbricht with DPR,
    the Laptop Warrant authorized agents to search for: “any communications or
    writings by Ulbricht, which may reflect linguistic patterns or idiosyncra[s]ies
    associated with ‘Dread Pirate Roberts,’ or political/economic views associated
    with [DPR] . . .”; “any evidence concerning any computer equipment, software,
    or usernames used by Ulbricht, to allow comparison with” computer equipment
    used by DPR; “any evidence concerning Ulbricht’s travel or patterns of
    movement, to allow comparison with patterns of online activity of [DPR]”; “any
    evidence concerning Ulbricht’s technical expertise concerning Tor, Bitcoins,” and
    other computer programming issues; any evidence concerning Ulbricht’s
    attempts to “obtain fake identification documents,” use aliases, or otherwise
    51
    evade law enforcement; and “any other evidence implicating Ulbricht in the
    subject offenses.” 
    Id. at 248-49
    (footnote omitted).
    After careful consideration of the warrant, the supporting affidavit, and
    Ulbricht’s arguments, we conclude that the Laptop Warrant did not violate the
    Fourth Amendment’s particularity requirement.34 We note, at the outset of our
    review, that the warrant plainly satisfies the basic elements of the particularity
    requirement as traditionally understood. By incorporating the affidavit by
    reference, the Laptop Warrant lists the charged crimes, describes the place to be
    searched, and designates the information to be seized in connection with the
    specified offenses. Each category of information sought is relevant to Silk Road,
    DPR’s operation thereof, or identifying Ulbricht as DPR. We do not understand
    Ulbricht’s arguments to contest the Laptop Warrant’s basic compliance with
    those requirements.35
    34
    The district court ruled that Ulbricht did not have standing to raise his Fourth
    Amendment challenges because he did not establish that he had a personal
    expectation of privacy in the laptop or his Facebook and Google accounts. We
    express no view on that issue, since the district court also reached the merits of
    the motion to suppress and the government has agreed that Ulbricht has
    standing to challenge the warrants and accompanying searches.
    35
    It is worth noting that Ulbricht does not challenge the validity of the search
    warrant covering his home, although that warrant is quite similar to the Laptop
    52
    Rather, Ulbricht’s arguments turn on the special problems associated with
    searches of computers which, as we have acknowledged in prior cases, 
    Galpin, 720 F.3d at 447
    ; 
    Ganias, 824 F.3d at 217-18
    , can be particularly intrusive. These
    arguments merit careful attention. For example, Ulbricht questions the
    appropriateness of the protocols that the Laptop Warrant instructed officers to
    use in executing the search. Those procedures included opening or “cursorily
    reading the first few” pages of files to “determine their precise contents,”
    searching for deliberately hidden files, using “key word searches through all
    electronic storage areas,” and reviewing file “directories” to determine what was
    relevant. S.A. 253. Ulbricht, supported by amicus the National Association of
    Criminal Defense Lawyers (“NACDL”), argues that the warrant was
    insufficiently particular because the government and the magistrate judge failed
    to specify the search terms and protocols ex ante in the warrant.
    We cannot agree. As illustrated by the facts of this very case, it will often
    be impossible to identify in advance the words or phrases that will separate
    relevant files or documents before the search takes place, because officers cannot
    Warrant and appears to be just as broad. Specifically, the home search warrant
    allows the government to search for and seize evidence concerning Ulbricht’s
    travel or patterns of movement and any of his communications or writings.
    53
    readily anticipate how a suspect will store information related to the charged
    crimes. Files and documents can easily be given misleading or coded names, and
    words that might be expected to occur in pertinent documents can be encrypted;
    even very simple codes can defeat a pre-planned word search. For example, at
    least one of the folders on Ulbricht’s computer had a name with the misspelling
    “aliaces.” App’x 309. For a more challenging example, Ulbricht also kept records
    of certain Tor chats in a file on his laptop that was labeled “mbsobzvkhwx4hmjt.”
    
    Id. at 398.36
    The agents reasonably anticipated that they would face such problems in
    this case. Operating Silk Road involved using sophisticated technology to mask
    its users’ identities. Accordingly, although we acknowledge the NACDL’s
    suggestions in its amicus submission for limiting the scope of such search terms,
    the absence of the proposed limitations does not violate the particularity
    36
    We note that Ulbricht and amicus NACDL somewhat exaggerate the novelty of
    computer searches in this regard. A traditional physical search for paper “drug
    records” or “tax records” may entail a similar examination of all sorts of files and
    papers to determine whether such records are hidden in files with innocuous or
    misleading names or written in coded terms to mask their content. For obvious
    reasons, search warrants authorizing the seizure of such evidence have not
    traditionally specified that agents may look only at file folders labeled “drug
    records” or may seize only papers containing the word “cocaine”—the
    equivalent of the ex ante “search terms” demanded by Ulbricht.
    54
    requirement on the facts of this case. We therefore conclude that, in preparing the
    Laptop Warrant, “law enforcement agents [did] the best that could reasonably be
    expected under the circumstances, [had] acquired all the descriptive facts which
    a reasonable investigation could be expected to cover, and [had] insured that all
    those facts were included in the warrant.” 
    Galpin, 720 F.3d at 446
    (internal
    quotation marks omitted).
    The fundamental flaw in Ulbricht’s (and the NACDL’s) argument is that it
    confuses a warrant’s breadth with a lack of particularity. As noted above, breadth
    and particularity are related but distinct concepts. A warrant may be broad, in
    that it authorizes the government to search an identified location or object for a
    wide range of potentially relevant material, without violating the particularity
    requirement. For example, a warrant may allow the government to search a
    suspected drug dealer’s entire home where there is probable cause to believe that
    evidence relevant to that activity may be found anywhere in the residence.
    Similarly, “[w]hen the criminal activity pervades [an] entire business, seizure of
    all records of the business is appropriate, and broad language used in warrants
    will not offend the particularity requirements.” U.S. Postal Serv. v. C.E.C. Servs.,
    
    869 F.2d 184
    , 187 (2d Cir. 1989). Ulbricht used his laptop to commit the charged
    55
    offenses by creating and continuing to operate Silk Road. Thus, a broad warrant
    allowing the government to search his laptop for potentially extensive evidence
    of those crimes does not offend the Fourth Amendment, as long as that warrant
    meets the three particularity criteria outlined above.
    It is also true that allowing law enforcement to search his writings for
    linguistic similarities with DPR authorizes a broad search of written materials on
    Ulbricht’s hard drive. That fact, however, does not mean that the warrants
    violated the Fourth Amendment. The Laptop Warrant clearly explained that the
    government planned to compare Ulbricht’s writings to DPR’s posts to confirm
    that they were the same person, by identifying both linguistic patterns and
    distinctive shared political or economic views. Ulbricht and the NACDL similarly
    claim that searching for all evidence of his travel patterns and movement violates
    the Fourth Amendment’s particularity requirement. Again, the warrant
    explained that it sought information about Ulbricht’s travel “to allow comparison
    with patterns of online activity of ‘Dread Pirate Roberts’ and any information
    known about his location at particular times.” S.A. 248. Thus, the Laptop Warrant
    56
    connects the information sought to the crimes charged and, more specifically, its
    relevance to identifying Ulbricht as the perpetrator of those crimes.37
    We remain sensitive to the difficulties associated with preserving a
    criminal defendant’s privacy while searching through his electronic data and
    computer hard drives. In the course of searching for information related to Silk
    Road and DPR, the government may indeed have come across personal
    documents that were unrelated to Ulbricht’s crimes. Such an invasion of a
    criminal defendant’s privacy is inevitable, however, in almost any warranted
    search because in “searches for papers, it is certain that some innocuous
    documents will be examined, at least cursorily, in order to determine whether
    37
    Evidence revealing a suspect’s past movements is often highly relevant to a
    criminal investigation. Such evidence might be used to establish—or rule
    out—the suspect’s presence at a crime scene or other pertinent location at a
    particular time. It may also disclose other, unrelated information about the
    suspect’s non-criminal associations, interests, and behavior, and may be drawn
    from a wide variety of sources. Government efforts to develop such information,
    including by search warrants authorizing its seizure, are not inherently
    questionable under the Fourth Amendment. Using piecemeal or laborious
    investigative techniques, it might take law enforcement officers a great deal of
    time and effort to compile a comprehensive record of a suspect’s travel or other
    movements. The fact that extensive travel records are stored on a digital device
    and may be accessed readily via a keystroke or quick search does not immunize
    those records from seizure. Indeed, the seizure of a paper journal or calendar in a
    conventional search will often allow officers to map out a defendant’s travel
    history with similar ease.
    57
    they are, in fact, among those papers authorized to be seized.” 
    Ganias, 824 F.3d at 211
    , quoting 
    Andresen, 427 U.S. at 482
    n.11. The Fourth Amendment limits such
    “unwarranted intrusions upon privacy,” 
    id. (internal quotation
    marks omitted),
    by requiring a warrant to describe its scope with particularity. The Laptop
    Warrant satisfied that requirement. Ulbricht has challenged only the facial
    validity of the Laptop Warrant and not its execution. Because we have no reason
    to doubt that the officers faithfully executed the warrant, its execution did not
    result in an undue invasion of Ulbricht’s privacy.
    Finally, we note that the crimes charged in this case were somewhat
    unusual. This case does not involve a more typical situation in which officers
    searched for evidence of a physician’s illegal distribution of pain medications, to
    use the NACDL’s example, which may have electronically-stored data associated
    with the alleged crimes on a hard drive that largely contains non-criminal
    information. Here the crimes under investigation were committed largely
    through computers that there was probable cause to believe included the laptop
    at issue, and the search warrant application gave ample basis for the issuing
    magistrate judge to conclude that evidence related to Silk Road and Ulbricht’s
    use of the DPR username likely permeated Ulbricht’s computer. Thus, given the
    58
    nature of Ulbricht’s crimes and their symbiotic connection to his digital devices,
    we decline to rethink the well-settled Fourth Amendment principles that the
    Laptop Warrant may implicate. A future case may require this Court to articulate
    special limitations on digital searches to effectuate the Fourth Amendment’s
    particularity or reasonableness requirements. Such a case is not before us.
    2. The Google and Facebook Warrants
    Ulbricht also challenges the warrants that allowed the government to
    search his Google and Facebook accounts, although he does not present any
    specific arguments related to those warrants. Both warrants, through affidavits
    incorporated by reference, set forth the basis for probable cause to search those
    accounts for evidence of Ulbricht’s involvement in Silk Road. The warrants also
    authorized the government to search his Google and Facebook accounts for
    “evidence, fruits, and instrumentalities” of the specified offenses, including, inter
    alia: “any communications or writings by Ulbricht”; “any evidence concerning
    any computer equipment, software, or usernames used by Ulbricht”; “any
    evidence concerning Ulbricht’s travel or patterns of movement”; and any “other
    evidence of the” crimes charged. S.A. 334-35, 393-94. The scope of the Google and
    Facebook warrants thus substantially paralleled that of the Laptop Warrant.
    59
    The Google and Facebook warrants were constitutional for the same
    reasons that the Laptop Warrant was valid. They satisfied all three of the
    particularity requirements because they listed the subject offenses, described the
    things to be searched, and identified the information to be seized in relation to
    the charged crimes. Ulbricht does not advance any additional arguments specific
    to the Google and Facebook warrants, nor have we identified any independent
    reason to find them unconstitutionally lacking in specificity.
    3. Conclusion
    In sum, the issuance of the pen/trap orders and the three search warrants
    that Ulbricht challenges in this appeal did not violate the Fourth Amendment.38
    Thus, we affirm the district court’s denial of Ulbricht’s suppression motion.
    II.   The District Court’s Trial Rulings and Ulbricht’s Rule 33 Motion
    Ulbricht contends that he did not receive a fair trial for several reasons:
    (1) the district court’s rulings surrounding corrupt agents Force and Bridges
    38
    The government also contends that, even if the warrants were invalid, the good
    faith exception prevents the application of the exclusionary rule. In general, the
    “exclusion of evidence is inappropriate when the government acts in objectively
    reasonable reliance on a search warrant, even when the warrant is subsequently
    invalidated.” 
    Ganias, 824 F.3d at 221
    (internal quotation marks omitted). Because
    we conclude that all three of the warrants were valid, we need not address the
    government’s alternative argument.
    60
    violated his due process rights; (2) the district court erroneously precluded two
    defense experts from testifying; (3) the district court abused its discretion when it
    curtailed Ulbricht’s cross-examination of two government witnesses; and (4) the
    district court erred when it ruled that certain hearsay statements were
    inadmissible. He also contends that, even if each individual error is harmless, the
    cumulative effect of those errors prejudiced him to the extent that his trial was
    fundamentally unfair. We detect no error in the district court’s rulings on any of
    those issues and therefore conclude that Ulbricht was not deprived of his right to
    a fair trial.
    A. Corrupt Agents Force and Bridges
    Ulbricht’s principal fair trial argument is that the district court erred in
    numerous ways by preventing him from relying on information related to the
    corruption of two federal agents, Force and Bridges, involved in the investigation
    of the Silk Road site. Before trial, the district court (1) precluded Ulbricht from
    referring at trial to the secret grand jury proceeding against Force; (2) denied
    Ulbricht discovery related to the Force investigation; and (3) denied Ulbricht an
    adjournment of the trial until the Force investigation was complete. During trial,
    the district court excluded as hearsay certain chats that related to Force’s illicit
    61
    use of Silk Road. Finally, Ulbricht learned after trial that the government was
    investigating a second corrupt agent, Bridges. Ulbricht contends that the failure
    to disclose Bridges’s corruption until after the trial violated Brady v. Maryland, 
    373 U.S. 83
    (1963), and that the district court erroneously denied his motion for a new
    trial on that ground.
    Without question, the shocking personal corruption of these two
    government agents disgraced the agencies for which they worked and
    embarrassed the many honorable men and women working in those agencies to
    investigate serious criminal wrongdoing. Even more importantly, when law
    enforcement officers abuse their offices for personal gain, commit other criminal
    acts, violate the rights of citizens, or lie under oath, they undermine the public’s
    vital trust in the integrity of law enforcement. They may also compromise the
    investigations and prosecutions on which they work.
    At the same time, the venality of individual agents does not necessarily
    affect the reliability of the government’s evidence in a particular case or become
    relevant to the adjudication of every case in which the agents participated. Courts
    are obligated to ensure that probative evidence is disclosed to the defense,
    carefully evaluated by the court for its materiality to the case, and submitted for
    62
    the jury’s consideration where admissible. But courts must also take care that
    wrongdoing by investigators that has no bearing on the matter before the court
    not be used as a diversion from fairly assessing the prosecution’s case. Like any
    other potential evidence, information about police corruption must be evaluated
    by reference to the ordinary rules of criminal procedure and evidence, a task to
    which we now turn.
    1. Background: Pretrial Disclosure of the Force Investigation
    The government disclosed its investigation into Force’s corruption to the
    defense about six weeks before trial. Initially, on November 21, 2014, the
    government wrote a sealed ex parte letter to the district court seeking permission
    to disclose to the defense information about the Force grand jury investigation
    subject to a protective order.39 The district court granted the application. On
    December 1, the government provided a copy of the November 21 letter, which
    otherwise remained sealed, to defense counsel. According to the letter, Force
    leaked information to DPR in exchange for payment and “corruptly obtain[ed]
    39
    The government required such an order because grand jury proceedings are
    secret and a government attorney “must not disclose a matter occurring before
    the grand jury,” Rule 6(e)(2)(B)(vi), Fed. R. Crim. P., without a court order, Rule
    6(e)(3)(E), subject to limited exceptions not relevant here.
    63
    proceeds from the Silk Road website and convert[ed] them to his personal
    use.”App’x 649. The government then undertook to purge its trial evidence of
    anything arguably traceable to Force.
    Ulbricht moved to unseal the entire November 21 letter so that he could
    rely on the information in the letter that related to Force’s corruption at trial,
    arguing that the letter included Brady information and that he therefore had a
    particularized need to disclose the information that outweighed the presumption
    of grand jury secrecy. He also requested discovery and subpoenas under Rules 16
    and 17, Fed. R. Crim. P., to learn more about the scope of Force’s corruption. In
    the alternative, Ulbricht sought an adjournment of the trial until the Force
    investigation concluded and information about his corruption might become
    public through the filing of charges against him. On December 15, the district
    court held a sealed hearing on that issue and invited further written submissions,
    including a particularized list of Ulbricht’s discovery requests. One week later,
    the district court issued a sealed and partially redacted opinion40 denying all of
    40
    Portions of the district court opinion were redacted because they referenced the
    defendant’s ex parte submissions explaining how he would use information
    related to the Force investigation at trial. This Court has reviewed an unredacted
    version of the district court opinion in connection with this appeal, but not the ex
    parte letters that the opinion references.
    64
    Ulbricht’s requests. The court did indicate, however, that throughout the trial it
    would “entertain specific requests to use information from the November 21,
    2014 Letter on cross-examination.” App’x 700. Moreover, the court explained that
    it would “entertain a renewed application” for a “particularized disclosure” of
    facts relevant to Force’s corruption if the government’s trial tactics or evidence
    “open[ed] the door” to such facts. 
    Id. 2. Preclusion
    of Force Investigation Evidence: Rule 6(e)
    On appeal, Ulbricht claims that the district court erred in denying his
    motion to unseal the November 21 letter because he demonstrated a
    particularized need that rebutted the presumption of secrecy that attaches to
    grand jury investigations. We disagree.
    “[T]he proper functioning of our grand jury system depends upon the
    secrecy of grand jury proceedings.” Douglas Oil Co. of California v. Petrol Stops
    Nw., 
    441 U.S. 211
    , 218 (1979). We have described five rationales for such secrecy:
    (1) To prevent the escape of those whose indictment
    may be contemplated; (2) to insure the utmost freedom
    to the grand jury in its deliberations, and to prevent
    persons subject to indictment or their friends from
    importuning the grand jurors; (3) to prevent
    subornation of perjury or tampering with the witnesses
    who may testify before the grand jury and later appear
    65
    at the trial of those indicted by it; (4) to encourage free
    and untrammeled disclosures by persons who have
    information with respect to the commission of crimes;
    (5) to protect the innocent accused who is exonerated
    from disclosure of the fact that he has been under
    investigation, and from the expense of standing trial
    where there was no probability of guilt.
    In re Grand Jury Subpoena, 
    103 F.3d 234
    , 237 (2d Cir. 1996). Rule 6(e)(6) of the
    Federal Rules of Criminal Procedure implements this policy of secrecy by
    requiring that “all records, orders, and subpoenas relating to grand jury
    proceedings [must] be sealed.” In re Grand Jury 
    Subpoena, 103 F.3d at 237
    (emphasis in original).
    Information falling within Rule 6(e)’s protections is entitled to a
    “presumption of secrecy and closure.” 
    Id. at 239.
    To rebut the presumption of
    secrecy, the party “seeking disclosure [must] show a particularized need that
    outweighs the need for secrecy.” 
    Id. (internal quotation
    marks omitted). To prove
    a particularized need, parties seeking disclosure must show that the “material
    they seek is needed to avoid a possible injustice in another judicial proceeding,
    that the need for disclosure is greater than the need for continued secrecy, and
    that their request is structured to cover only material so needed.” 
    Id. (internal quotation
    marks omitted). “A district court’s decision as to whether the burden of
    66
    showing a particularized interest has been met will be overturned only if the
    court has abused its discretion.” 
    Id. We cannot
    say that the district court abused its discretion when it denied
    Ulbricht’s request to unseal the November 21 letter discussing the Force grand
    jury investigation. It is undisputed that the letter contained information related to
    a grand jury proceeding that, if made public, would disclose matters occurring
    before the grand jury. Ulbricht did not demonstrate a particularized need for
    disclosure because he did not show that the need for disclosure was greater than
    the need for continued secrecy or that a possible injustice would result if the
    grand jury investigation was not disclosed. Specifically, the district court did not
    err in concluding that revealing the entire letter could have compromised the
    Force grand jury investigation in a number of ways. For example, potential co-
    conspirators might have learned of the investigation and attempted to intimidate
    witnesses or destroy evidence. The investigation was also likely to garner
    significant media attention, a fact that might influence witnesses or grand jurors.
    And, although Force knew of the investigation, revealing its existence to the
    public might have harmed him if the allegations had ultimately proved untrue.
    Finally, Ulbricht’s request was not structured to cover only the information
    67
    needed to avoid any possible injustice; instead, he sought to unseal the entire
    November 21 letter and did not propose a more narrowly tailored disclosure.
    In redacted portions of its opinion, the district court also considered ex
    parte arguments concerning how the Force investigation might be relevant to
    Ulbricht’s defense. In general terms, Ulbricht argued that the agents’ corruption
    was critical to his defense because it would reveal the agents’ ability to falsify
    evidence against him and demonstrate their motive to do so. According to the
    district court’s characterization of his ex parte letters, Ulbricht speculated that
    Force may have used Curtis Green’s (Flush) administrative capabilities to
    impersonate DPR; Force’s corrupt conduct might have demonstrated technical
    vulnerabilities in the site that would render it susceptible to hacking; and
    learning that Force had good information about the Silk Road investigation might
    have caused the true DPR to recruit Ulbricht as his successor.41
    41
    As noted above, see note 5, we have carefully considered to what extent it is
    appropriate to refer to portions of the record that remain under seal. We have
    been especially careful in describing the portions of the district court’s opinion
    that remain redacted and therefore are still not available to the government or to
    the public. We appreciate that charges against Ulbricht remain pending in
    Maryland and that the redacted information describes what would have been his
    trial strategy had he been able to reference Force’s corruption. We have thus
    described the defense’s redacted arguments at a fairly high level of generality.
    We are confident that any experienced prosecutor could anticipate those
    68
    The district court reasoned that much of the information that might have
    arguably supported any of those theories was made available to the defense in
    discovery. The only new information in the November 21 letter concerned the
    investigation of Force’s corruption; the fact of that investigation and its scope
    does not bolster any of the defense theories that Ulbricht described before the
    district court or on appeal. That Force was personally corrupt and used his
    undercover identity to steal money from Silk Road and DPR does not suggest
    either a motive or an ability on his part to frame Ulbricht as DPR. Absent any
    explanation of how Force could have orchestrated a massive plant of
    incriminating information on Ulbricht’s personal laptop, his larcenous behavior
    does not advance the claim that such a frame-up was possible beyond mere
    arguments, and that in any event the information is largely stated or implied in
    Ulbricht’s own publicly filed briefs on appeal. Particularly given that our
    description relates to how the Force information might have been used at a trial
    that is now completed, and that we now hold that Ulbricht is not entitled to a
    new trial, we conclude that the public’s need to understand and evaluate
    Ulbricht’s arguments that he was unfairly prejudiced by the district court’s
    rulings, as well as our reasons for rejecting those arguments, outweighs any
    minimal interest that Ulbricht might have in withholding his contentions from
    the government.
    69
    speculation. Thus, Ulbricht was equally capable of presenting his various defense
    theories to the jury with or without the November 21 letter.42
    The government’s commitment to eliminating all evidence that came from
    Force’s work on the Silk Road investigation43 further undermines Ulbricht’s claim
    that he needed the information to avoid a possible injustice. Had Force been
    called as a government witness, or had any of the government’s evidence relied
    on his credibility, his character for truthfulness would have been at issue during
    the trial, and information that impeached his credibility would have become
    highly relevant. Ulbricht’s reliance on the general fact of cooperation among
    different government agencies and different U.S. Attorney’s Offices does not
    undermine the government’s explicit representations that none of the evidence
    presented at trial derived from Force, and nothing in the record suggests that
    42
    Even on appeal, moreover, after the disclosure of additional information in the
    prosecutions of Bridges and Force, Ulbricht does not provide any concrete
    explanation of how the techniques used by the corrupt agents to steal money
    from Silk Road could have been used, by them or by others, to plant the massive
    amounts of incriminating information found on Ulbricht’s laptop and in his
    house.
    43
    For example, the government declined to present evidence of DPR’s attempt to
    commission an additional murder because that conduct involved Force acting as
    Nob.
    70
    those representations were false. Ulbricht had no need to rely on the grand jury
    investigation of Force to attack the credibility of the actual government witnesses
    or the integrity of its other evidence.
    In sum, Ulbricht has not shown that the district court abused its discretion
    in maintaining the secrecy of the Force grand jury investigation. He did not
    demonstrate to the district court, and has not demonstrated on appeal, that
    keeping the November 21 letter under seal resulted in any injustice, or that his
    need for disclosing the investigation was greater than the need for continued
    secrecy.44
    3. Denial of Discovery Related to Force
    Ulbricht claims that the district court erred in denying him discovery,
    including requested subpoenas, related to the Force investigation. Rule
    16(a)(1)(E), Fed. R. Crim. P., requires the government to disclose information
    within its control if the information is “material to preparing the defense” or will
    44
    Moreover, the district court specifically ruled that it would entertain Ulbricht’s
    applications to rely on specific parts of the letter at trial if doing so would be
    necessary for effective cross-examination. Thus, Ulbricht was given the
    opportunity to show particularized need in the context of specific trial evidence.
    Ulbricht has not identified any point in the trial where he attempted to show that
    Force’s behavior had become relevant to challenging the credibility of particular
    aspects of the prosecution’s case.
    71
    be a part of the government’s case-in-chief. Evidence is material if it “could be
    used to counter the government’s case or to bolster a defense.” United States v.
    Stevens, 
    985 F.2d 1175
    , 1180 (2d Cir. 1993). “An appellate court, in assessing the
    materiality of withheld information, considers not only the logical relationship
    between the information and the issues in the case, but also the importance of the
    information in light of the evidence as a whole.” 
    Id. To justify
    a new trial, there
    “must be some indication that the pretrial disclosure of the disputed evidence
    would have enabled the defendant significantly to alter the quantum of proof in
    his favor.” 
    Id. (internal quotation
    marks omitted).
    Rule 17(c), Fed. R. Crim. P., allows parties to subpoena documents and
    objects to be introduced at criminal trials. A subpoena must meet three criteria:
    “(1) relevancy; (2) admissibility; [and] (3) specificity.” United States v. Nixon, 
    418 U.S. 683
    , 700 (1974). The party requesting the subpoena must also show that the
    information sought is “not otherwise procurable reasonably in advance of trial by
    exercise of due diligence,” that “the party cannot properly prepare for trial
    without such production,” and that “the application is made in good faith and is
    not intended as a general ‘fishing expedition.’” 
    Id. at 699-700.
    We review the
    72
    district court’s discovery rulings for abuse of discretion. United States v. Rigas, 
    583 F.3d 108
    , 125 (2d Cir. 2009).
    The district court did not abuse its discretion when it denied Ulbricht’s
    discovery requests related to the Force investigation. Ulbricht submitted 28
    individual discovery requests in connection with the Force disclosure. Those
    ranged from the reasonably specific, such as “records from any and all Bitcoin
    accounts” used by Force, to the very broad, such as “any spending, net worth, or
    other financial analysis conducted with respect to former SA Force,” “any and all
    phone records relating to former SA Force,” and “bank account records from any
    and all bank accounts maintained by former SA Force or his spouse.” App’x 669-
    70. The district court concluded that those requests were too broad and
    unfocused, and that the information requested was not material in the Rule 16
    sense because the defense “has not articulated a coherent and particular reason
    why” the Force investigation could “counter the government’s case or bolster a
    defense.” 
    Id. at 697.
    Next, the district court concluded that the Rule 17 subpoenas
    were part of the same overall fishing expedition and that the issuance of such
    subpoenas could compromise the Force grand jury investigation.
    73
    There was no abuse of discretion in those rulings. Ulbricht has not shown
    that, had the government produced every piece of requested information, he
    would have been able to alter the quantum of proof in his favor at trial. That is so
    because there is no indication, beyond Ulbricht’s speculation, that Force
    manufactured any of the evidence on which the government relied at trial, let
    alone the most damning evidence discovered on the hard drive on Ulbricht’s
    laptop and at his apartment. Because Force did not testify at trial, information
    related to his corruption would not have been relevant to attack the credibility of
    any testimony he would have given. Moreover, Ulbricht has not identified any
    specific aspect of the trial evidence that he could have undermined using the
    requested information. Thus, even if the district court erred in not granting at
    least some of Ulbricht’s discovery requests, any such error does not justify a new
    trial.
    4. Ulbricht’s Motion to Adjourn the Trial
    Ulbricht contends that the district court erred in denying his request to
    adjourn the trial until the Force investigation was complete. “[A] district court
    has a great deal of latitude in scheduling trials.” United States v. Griffiths, 
    750 F.3d 237
    , 241 (2d Cir. 2014) (internal quotation marks omitted). Thus, “trial courts
    74
    enjoy very broad discretion in granting or denying trial continuances.” United
    States v. Stringer, 
    730 F.3d 120
    , 127 (2d Cir. 2013). A decision to grant or deny a
    request for an adjournment is reviewed for abuse of discretion, and we “will find
    no such abuse unless the denial was an arbitrary action that substantially
    impaired the defense.” 
    Id. (internal quotation
    marks omitted). Thus, the party
    seeking a continuance has the burden of showing “both arbitrariness and
    prejudice in order to obtain reversal” based on a denial of an adjournment. 
    Id. at 128
    (internal quotation marks omitted).
    The district court did not abuse its discretion in denying Ulbricht’s request
    for an adjournment of the trial. In a sealed portion of the proceedings on the first
    day of trial, the district court explained its reasons for denying the adjournment.
    The court ruled that because none of the evidence revealed by the government
    concerning Force’s corruption was exculpatory, there was no reason to believe
    that delaying the trial would assist Ulbricht’s defense. That analysis was not
    irrational or arbitrary. Moreover, as explained in more detail both above and
    below, Ulbricht has not shown how information related to Force’s corruption was
    either exculpatory or material to his defense. Thus, he has not shown that the
    75
    district court’s refusal to adjourn the trial was prejudicial, let alone substantially
    so.
    5. Preclusion of the DeathFromAbove Chats
    As already described, Force used DeathFromAbove as an unauthorized
    Silk Road username through which he attempted to extort money from DPR. The
    government only learned of Force’s activity as DeathFromAbove during trial,
    when the defense attempted to introduce a redacted chat between DPR and
    DeathFromAbove. In the chat at issue, DeathFromAbove implied that he knew
    that DPR’s real identity was Anand Athavale. DeathFromAbove then attempted
    to blackmail DPR by saying that, if DPR gave him $250,000, he would not “give
    you [sic] identity to law enforcement.” App’x 712.
    The government objected to admitting the chat on three grounds: (1) it was
    hearsay; (2) its probative value was substantially outweighed by unfair prejudice
    under Rule 403, Fed. R. Evid.; and (3) it was a “back-door attempt to re-inject”
    Force’s corruption into the defense’s trial evidence. App’x 707. The district court
    excluded the chat as hearsay. At trial, Ulbricht claimed that the chat was not
    being offered for its truth, but instead to show its effect on DPR; that is, if DPR
    was actually Athavale, one would expect DPR to take certain steps to protect his
    76
    identity. The district court disagreed and ruled that the DeathFromAbove chat
    was hearsay because it was offered for the truth of the matter asserted
    therein—that government agents at one time thought that Athavale was
    DPR—and it did not fall into any hearsay exceptions. In the alternative, the
    district court found that the Athavale-as-DPR theory lacked sufficient support,
    was speculative, and risked jury confusion.
    In general, hearsay is not admissible unless an exception applies. See Fed.
    R. Evid. 802. “The Federal Rules of Evidence define hearsay as a declarant’s
    out-of-court statement offered in evidence to prove the truth of the matter
    asserted in the statement.” United States v. Dupree, 
    706 F.3d 131
    , 136 (2d Cir. 2013)
    (internal quotation marks and alterations omitted). If “the significance of an
    offered statement lies solely in the fact that it was made, no issue is raised as to
    the truth of anything asserted, and the statement is not hearsay.” 
    Id. (internal quotation
    marks omitted). “The trial court’s ultimate decisions as to the
    admission or exclusion of evidence are reviewed for abuse of discretion.” Davis v.
    Velez, 
    797 F.3d 192
    , 201 (2d Cir. 2015).
    The district court concluded that the DeathFromAbove chat was hearsay
    because it was an out-of-court statement being offered for the truth of the matter
    77
    asserted therein. That ruling was not an abuse of discretion. Contrary to
    Ulbricht’s assertions on appeal, the district court did not rest its decision on the
    need for grand jury secrecy to protect the Force investigation. Instead, the
    decision was a straightforward application of the rule against hearsay.
    Ulbricht does not provide any detailed arguments to the contrary that are
    specific to the DeathFromAbove chat; instead, he discusses the district court’s
    preclusion of all of the evidence related to the Force investigation collectively. At
    trial, however, he claimed that the statement was offered only to demonstrate
    “the fact that it was communicated to DPR . . . in that this particular piece of
    evidence communicates to DPR the name and profile of the person
    [D]eath[F]rom[A]bove believes is DPR.” Tr. 1866. Ulbricht claimed that the
    statement was “offered for the fact that DPR was getting information about
    people who were supposed to be DPR,” and “one of these people is [Athavale].”
    
    Id. at 1867.
    Once the district court expressed skepticism about his argument,
    Ulbricht claimed that he sought to admit the chat to demonstrate its effect on
    DPR: “if you’re DPR and you get a name . . . this Anand Athavale and a profile
    and details . . . and you’re put on notice that it’s you, you’re going to take steps.”
    
    Id. at 1867-68.
    In other words, Ulbricht claimed that he did not offer it for the
    78
    truth of the matter asserted in the chat: that agents in the Baltimore investigation,
    including Force, believed that Athavale was the real Dread Pirate Roberts, or that
    Athavale was in fact the real DPR.
    Ulbricht’s proposed non-hearsay use of the chat—to show its effect on
    DPR—is not sufficiently probative that the evidence’s exclusion prejudiced him.
    The statement does not appear to have had an effect on DPR that would bolster
    Ulbricht’s defense. DPR did not alter his behavior in response to the extortion
    attempt. Indeed, he referred to it as “bogus” in one of the journal entries
    discovered on Ulbricht’s laptop. App’x 710. If Athavale had been the real Dread
    Pirate Roberts, he likely would have had a different reaction to the threatened
    exposure of his identity. DPR’s reactions to other attempts to destroy the site’s
    anonymity were dramatic, and included hiring people to kill the users who
    threatened to compromise Silk Road. Therefore, even if Ulbricht did not offer the
    chat for its truth, any relevance of the arguably non-hearsay use of the statement
    was entirely too remote to outweigh the possible jury confusion that would result
    from the injection of Force into the trial or the likelihood that the jury would
    confuse the hearsay and non-hearsay significance of the evidence.
    79
    6. Ulbricht’s Rule 33 Motion: Brady v. Maryland
    Ulbricht moved for a new trial under Rule 33, Fed. R. Crim. P., raising
    several issues concerning the unfairness of the assertedly belated disclosures of
    the investigations into Force and Bridges.45 The only argument that he pursues in
    this appeal is that the belated disclosures violated his due process rights under
    Brady because the information was both material and exculpatory.
    Rule 33(a) provides that, on “the defendant’s motion, the court may vacate
    any judgment and grant a new trial if the interest of justice so requires.” We have
    advised district courts to “exercise Rule 33 authority sparingly and in the most
    extraordinary circumstances.” United States v. Coté, 
    544 F.3d 88
    , 101 (2d Cir. 2008)
    (internal quotation marks omitted). “Where a defendant’s Brady claim was raised
    in a motion for a new trial pursuant to Rule 33[,] . . . we review the denial of the
    motion for abuse of discretion.” United States v. Douglas, 
    525 F.3d 225
    , 245 (2d Cir.
    2008) (internal quotation marks omitted). In the context of denying a Rule 33
    motion, a “district court abuses . . . the discretion accorded to it when (1) its
    45
    Ulbricht filed his Rule 33 motion on March 6, 2015. The criminal complaint
    against Force and Bridges was unsealed on March 30, which is the first time that
    Ulbricht learned that Bridges was corrupt and was involved in the case.
    80
    decision rests on an error of law . . . or a clearly erroneous factual finding, or (2)
    its decision—though not necessarily the product of a legal error or a clearly
    erroneous factual finding—cannot be located within the range of permissible
    decisions.” United States v. Forbes, 
    790 F.3d 403
    , 406 (2d Cir. 2015) (internal
    quotation marks omitted).
    There are three components of a Brady violation: “(1) The evidence at issue
    must be favorable to the accused, either because it is exculpatory or because it is
    impeaching; (2) that evidence must have been suppressed by the [government],
    either willfully or inadvertently; and (3) prejudice must have ensued.” United
    States v. Certified Envtl. Servs., Inc., 
    753 F.3d 72
    , 91 (2d Cir. 2014) (internal
    quotation marks omitted). Information is exculpatory if it relates to the
    defendant’s guilt or innocence. United States v. Avellino, 
    136 F.3d 249
    , 255 (2d Cir.
    1998). In order to show that he has been prejudiced, a defendant must
    demonstrate “a reasonable probability that, had the evidence been disclosed, the
    result of the proceeding would have been different, such that the failure to
    disclose undermines confidence in the verdict.” Certified Envtl. Servs., 
    Inc., 753 F.3d at 91
    (internal quotation marks and alterations omitted). Thus, the
    prosecution “must disclose . . . exculpatory and impeachment information no
    81
    later than the point at which a reasonable probability will exist that the outcome
    would have been different if an earlier disclosure had been made.” 
    Id. at 92
    (internal quotation marks omitted). In general, a “prudent prosecutor will err on
    the side of transparency, resolving doubtful questions in favor of disclosure.”
    Cone v. Bell, 
    556 U.S. 449
    , 470 n.15 (2009).
    Although the agents’ illegal behavior in connection with the Silk Road
    investigation is deeply troubling, the government’s December 2014 disclosure of
    the Force investigation and the post-trial disclosure of Bridges’s corruption did
    not violate Ulbricht’s due process rights. Evidence concerning the agents’
    corruption is not Brady information because it is not exculpatory or impeaching
    of the government’s trial evidence. For this reason, the government’s failure to
    reveal the full extent of the investigations until after Ulbricht’s trial did not
    prejudice him. As already explained, the fact that Force purloined Bitcoins from
    Silk Road and attempted to blackmail DPR does not relate to Ulbricht’s guilt or
    innocence; the same logic applies to Bridges’s similar behavior. The agents’
    corruption has nothing to do with whether Ulbricht operated the site as Dread
    Pirate Roberts. Ulbricht has not raised any credible doubts about the reliability of
    the evidence that the government presented at trial, nor has he explained why
    82
    the agents’ illegal actions relate to his guilt at all. Indeed, the government
    removed from its exhibit list the items relevant to Force, including
    communications between Nob (his authorized undercover username) and DPR.
    Those communications included an instance in which DPR hired Nob to kill
    Curtis Green (Flush) as punishment for using his administrator status to steal
    Bitcoins from Silk Road users. Ulbricht does not identify any particular evidence
    introduced by the government at trial that is traceable to either Force or Bridges,
    or the admissibility of which depends on either agent’s integrity.
    Ulbricht’s arguments to the contrary largely rest on speculation. First,
    Ulbricht contends that the Silk Road investigations occurring in Baltimore and
    New York were “[c]oordinated and [c]ombined,” suggesting that Force’s
    corruption may have somehow infected the evidence that the New York office
    used in its prosecution. Appellant Br. 40. Ulbricht explains that the offices
    communicated frequently and shared information through emails and reports.
    Assuming that Ulbricht is correct, the fact that the Silk Road investigation took
    place in several offices, one of which employed two corrupt agents, does not alter
    our analysis. Ulbricht still has not shown how the agents’ corrupt behavior is
    exculpatory as to him, even if Force and Bridges at times shared their work
    83
    product with New York and that work product influenced the larger
    investigation. The relevant question, on which none of Ulbricht’s arguments casts
    any light or raises any doubt, is whether any particular item of evidence was
    tainted in some way by the misconduct of Bridges or Force.
    Next, Ulbricht surmises that the agents may have fabricated evidence
    suggesting that Ulbricht was DPR. In so arguing, Ulbricht implies that Force and
    Bridges may have had sufficiently high-level administrator access to Silk Road to
    manipulate the “financial, transactional, and communications infrastructure of
    the Silk Road site.” Reply Br. 14. Nothing in the government’s disclosures, and
    nothing that Ulbricht identifies in the record or has produced from any
    independent source, suggests that either Bridges or Force had such capacity.
    Absent further detail or evidence that Force and Bridges were able to infiltrate
    DPR’s communications or transactions, Ulbricht’s argument is simply too
    speculative to warrant a new trial. Ulbricht further claims that Bridges used
    sophisticated techniques to try to place blame on others for his corrupt conduct,
    reflecting a pattern of framing others for his own crimes. That fact alone does not
    suggest that Bridges fabricated any evidence against Ulbricht or attempted to
    frame him. That Bridges undertook to deflect blame for things he had done does
    84
    not suggest any reason why Bridges would be motivated to frame Ulbricht for
    things that DPR had done. Nor does Ulbricht explain how Bridges’s actions
    should undermine our confidence in any of the specific evidence on which the
    government relied at trial.46
    Finally, Ulbricht submitted a supplemental appendix that included a
    newly-discovered, unredacted report from the Joint Automated Booking System
    (“JABS”).47 In that report, under the heading “Arrested or Received Information,”
    Force is listed as the officer on the case, and the Baltimore DEA is listed as the
    relevant agency. Ulbricht apparently means to suggest that this report shows that
    Force played a more pervasive role in the investigation than the government has
    acknowledged. In response, the government argues that Force was simply the
    46
    In a footnote, Ulbricht claims that failing to disclose the full extent of the
    agents’ corruption deprived him of an opportunity to “attack[] the investigation
    as shoddy.” Kyles v. Whitley, 
    514 U.S. 419
    , 442 n.13 (1995). Now that he has all of
    the relevant information, he still does not explain how he might have
    demonstrated deficiencies in the government’s investigation of his or one of the
    other initial suspects’ conduct that would undermine our confidence in the
    verdict.
    47
    As the government explains, and Ulbricht does not dispute, JABS is a database
    maintained by the United States Marshals Service that catalogues information
    regarding alleged offenders who have been arrested and booked by federal, state,
    or local law enforcement agencies.
    85
    most recent person to make changes to the JABS report by updating it to include
    information about Ulbricht’s family members and the pending charges in
    Maryland. In any event, the JABS report bearing Force’s name does not show
    how information related to Force’s corruption exculpates Ulbricht. It merely
    confirms that Force was a participant in the Baltimore Silk Road investigation
    and that he continued to be involved in the case after Ulbricht was arrested. In
    the face of the entire record of the trial, in which the provenance of the
    government’s evidence was exhaustively displayed without indication that Force
    was responsible for any of it, this single report has little or no probative value.
    In sum, we conclude that the Force and Bridges complaint did not contain
    Brady information because the agents’ corruption does not bear on Ulbricht’s
    guilt or innocence. Thus, any delay in the government’s disclosure of their
    corruption did not violate Ulbricht’s due process rights.
    B. Preclusion of Defense Experts
    The district court precluded both of Ulbricht’s proposed expert witnesses
    from testifying because he did not timely or adequately disclose his intent to call
    them under Rule 16, Fed. R. Crim. P. In general, the “defendant must, at the
    government’s request, give to the government a written summary of any [expert]
    86
    testimony that a defendant intends to use. . . . This summary must describe the
    witness’s opinions, the bases and reasons for those opinions, and the witness’s
    qualifications.”48 Fed. R. Crim. P. 16(b)(1)(C). The purpose of the expert
    disclosure requirement is to “minimize surprise that often results from
    unexpected expert testimony, reduce the need for continuances, and to provide
    the opponent with a fair opportunity to test the merit of the expert’s testimony
    through focused cross-examination.” Fed. R. Crim. P. 16, advisory committee’s
    note to 1993 amendment. Indeed, “[w]ith increased use of both scientific and
    nonscientific expert testimony, one of counsel’s most basic discovery needs is to
    learn that an expert is expected to testify.” 
    Id. If a
    party fails to comply with Rule 16, the district court has “broad
    discretion in fashioning a remedy,” which may include granting a continuance or
    “ordering the exclusion of evidence.” United States v. Lee, 
    834 F.3d 145
    , 158 (2d
    Cir. 2016) (internal quotation marks omitted); see Fed. R. Crim. P. 16(d)(2)(A)-(D)
    (a district court may order “any other [remedy] that is just under the
    circumstances”). We thus review the district court’s choice of remedy for abuse of
    48
    It is undisputed that the government requested such disclosure on December
    29, 2014, two weeks before trial began.
    87
    discretion. “In considering whether the district court abused its discretion, we
    look to the reasons why disclosure was not made, the extent of the prejudice, if
    any, to the opposing party, the feasibility of rectifying that prejudice by a
    continuance, and any other relevant circumstances.” 
    Lee, 834 F.3d at 159
    (internal
    quotation marks omitted).
    The district court did not abuse its discretion in precluding the defense
    from calling its proposed experts. Not only were the disclosures late, more
    importantly, they were plainly inadequate. Both disclosures merely listed general
    and in some cases extremely broad topics on which the experts might opine. For
    example, the disclosures indicated that the experts would testify on general
    topics, including: “the origins of Bitcoin,” “the various purposes and uses of
    Bitcoin,” “the mechanics of Bitcoin transactions,” “the value of Bitcoin over time
    since its inception,” “the concepts of Bitcoin speculating and Bitcoin mining,”
    “[g]eneral principles of internet security and vulnerabilities,” the “import of
    some lines of PHP code provided to defense counsel in discovery,” and
    “[g]eneral principles of public-key cryptography,” among others. App’x 349, 360.
    They did not summarize the experts’ opinions about those topics, let alone
    describe the bases for the experts’ opinions.
    88
    Indeed, although the listed topics certainly pertained generally to Silk
    Road, the disclosures were so vague that it is difficult to discern whether the
    proffered expert testimony would have been at all relevant under Rules 401 and
    702(a), Fed. R. Evid.49 In his opposition to the government’s motion to preclude
    Antonopoulos, Ulbricht described the expert’s proposed testimony in more
    detail, but he still did not disclose the opinions that the expert intended to offer.
    For example, that supplemental disclosure indicated that an “[i]ndependent
    defense investigation has uncovered that” the government’s claim that over
    700,000 Bitcoins were transferred to Ulbricht’s Bitcoin wallet “is implausible,”
    and the expert would “dispute this finding.” App’x 382. Although that is more
    specific, it is not a summary of Antonopoulos’s opinion, nor does it identify the
    basis for that opinion. Thus, to this day Ulbricht has not described what opinions
    49
    In particular, Ulbricht’s disclosures did not discuss, and he has not described
    on appeal, how one expert’s proposed testimony on “[g]eneral principles of
    internet security and vulnerabilities” would have linked to the defense claim that
    the damning documentary evidence of Ulbricht’s guilt found on his laptop was
    or could have been fabricated or planted. The jury was aware from other
    evidence, and indeed it is within ordinary lay experience, that various forms of
    hacking are possible. What was lacking, what the defense expert disclosures did
    not purport to address, and what Ulbricht still has not provided on appeal, is any
    explanation, let alone a credible explanation, of how the breadth and variety of
    information, from the laptop and other sources, could have been planted.
    89
    the experts would offer or explained the methods they used to arrive at any of
    those conclusions.
    The district court also did not abuse its discretion in finding that the
    government would be prejudiced by the belated and inadequate disclosures, in
    part because the government was due to rest the following day, providing it with
    no time to prepare to respond to the experts. Moreover, the district court
    considered intermediate sanctions short of preclusion but found them to be
    inadequate. In rejecting a continuance as a possible remedy, the district court
    emphasized the “known issues with a continuance,” especially in a lengthy trial.
    
    Id. at 369.
    Two of the jurors had time constraints, and a continuance might have
    caused the court to lose one or both of those jurors, especially if the continuance
    was lengthy. If it were to grant a continuance, the court would also need to
    perform its function as a gatekeeper of expert testimony under Daubert v. Merrell
    Dow Pharm., Inc., 
    509 U.S. 579
    , 592-93 (1993), which requires the district court to
    make a “preliminary assessment of whether the reasoning or methodology
    underlying the [expert] testimony is scientifically valid” and “can be applied to
    90
    the facts in issue.”50 The district court cannot perform that complex evaluation of
    an expert’s proposed methodology without a clear articulation of what the
    expert’s opinions are and, even more importantly, of the bases for those opinions.
    In light of the risk of losing jurors and the lack of a sufficiently compelling reason
    for the defense’s clear violation of Rule 16, the district court was within its
    discretion when it determined that a continuance was not practical and that the
    appropriate remedy was to preclude the witnesses altogether.
    Ulbricht’s arguments to the contrary are not persuasive. First, Ulbricht
    argues that the two experts were necessary to rebut portions of the government’s
    case that he was precluded from addressing during cross-examination, as well as
    the testimony of Ilhwan Yum, a government witness who analyzed transactions
    50
    We have explained that a Daubert reliability assessment requires a district court
    to consider the “extent to which [the expert’s theory] has been subjected to peer
    review and publication,” whether the technique is “subject to standards
    controlling the technique’s operation,” the “known or potential rate of error,”
    and the “degree of acceptance within the relevant scientific community.” United
    States v. Romano, 
    794 F.3d 317
    , 330 (2d Cir. 2015) (internal quotation marks
    omitted). That inquiry is a “flexible one,” however, and Daubert is not a
    “definitive checklist or test” for the reliability of expert testimony. 
    Id. (internal quotation
    marks omitted). Thus, “[w]hether Daubert’s specific factors are, or are
    not, reasonable measures of reliability in a particular case is a matter that the law
    grants the trial judge broad latitude to determine.” 
    Id. at 331
    (internal quotation
    marks omitted).
    91
    associated with Bitcoin wallets found on Ulbricht’s laptop. Ulbricht now
    contends that portions of Yum’s testimony were incorrect, including his
    description of what a “hot” Bitcoin wallet is.51 Ulbricht does not, however,
    explain how Yum’s testimony was incorrect, what contrary evidence his experts
    would have provided had they been allowed to testify, or how any purported
    correction of Yum’s testimony would have affected the case against Ulbricht. Nor
    has he produced any summaries of his proposed expert testimony or described
    how that testimony would have been material to Ulbricht’s guilt or innocence. In
    other words, Ulbricht has not shown that precluding Bellovin and Antonopoulos
    from testifying prejudiced him. Ulbricht’s alternative argument that the
    disclosures were in fact adequate is incorrect for the reasons already explained.
    Ulbricht next argues that preclusion was an unduly harsh remedy under
    the circumstances. Along those lines, he claims that certain exhibits, such as the
    summary chart on which Yum relied, were not produced until mid-trial. Thus,
    51
    “The terms hot wallet and cold wallet derive from the more general terms hot
    storage, meaning online storage, and cold storage, meaning offline storage. A hot
    wallet is a Bitcoin wallet for which the private keys are stored on a network-
    connected machine (i.e.[,] in hot storage). By contrast, for a cold wallet the private
    keys are stored offline.” Steven Goldfeder et al., Securing Bitcoin Wallets via a New
    DSA/ECDSA Threshold Signature Scheme, Princeton University 10, available at
    http://www.cs.princeton.edu/~stevenag/threshold_sigs.pdf.
    92
    according to Ulbricht, he could not have known about his need for expert
    witnesses to counter specific trial exhibits until it was already too late to comply
    with Rule 16. In his view, the district court should not have held him so strictly to
    Rule 16’s requirements because he could not have known until Yum testified that
    he would need to call an expert.
    While Ulbricht is correct that excluding his experts was a harsh sanction
    and was not to be imposed lightly, the district court considered the possibility of
    granting a continuance or a more limited sanction and found those remedies to
    be inappropriate under the circumstances. Such careful consideration of a range
    of possible sanctions short of preclusion is especially important in the atypical
    case where a criminal defendant, rather than the government, is precluded from
    putting on his case because of a Rule 16 violation. Limiting the defense’s
    presentation of his case implicates the fundamental right of “an accused to
    present witnesses in his own defense.” Chambers v. Mississippi, 
    410 U.S. 284
    , 302
    (1973). However, the defendant must still “comply with established rules of
    procedure and evidence designed to assure both fairness and reliability in the
    ascertainment of guilt and innocence.” 
    Id. Here, Ulbricht
    did not comply with the
    procedural requirements associated with expert disclosures. The district court
    93
    gave the issue due consideration and appropriately exercised its discretion in
    remedying the defense’s Rule 16 violation.
    Finally, Ulbricht cannot credibly argue that Yum’s testimony was the first
    notice he had about the possible need for an expert witness to testify as part of
    his affirmative case. The Silk Road prosecution was uniquely laden with issues
    related to technology, computer servers, forensics, cyber security, digital
    currency, and myriad other issues that are indisputably “beyond the ken of the
    average juror.” United States v. Mejia, 
    545 F.3d 179
    , 191 (2d Cir. 2008) (internal
    quotation marks omitted). Ulbricht surely knew from the outset that, in order to
    mount a meaningful attack on the government’s voluminous and technically
    complex evidence, he would need to call his own expert. Indeed, in his opening
    statement, Ulbricht’s counsel claimed that he would show that the Bitcoins in
    Ulbricht’s wallet were from innocent transactions associated with Bitcoin
    speculation, rather than, as the government contended, related to Silk Road.52
    52
    No evidence about the source of those Bitcoins was in fact presented by
    Ulbricht, and neither the expert disclosures presented to the district court nor
    Ulbricht’s arguments on appeal suggest that either Bellovin or Antonopoulos
    would have provided an analysis or explanation of Ulbricht’s Bitcoin transactions
    that would have revealed a non-Silk Road source for Ulbricht’s Bitcoins.
    94
    Ulbricht’s opening statement also implied that BitTorrent’s53 security deficiencies
    could have allowed the true DPR to plant incriminating evidence on his laptop. It
    is difficult to fathom how he planned to advance those theories without relying
    on expert testimony.
    In short, Ulbricht argues that the district court’s preclusion of his proffered
    expert witnesses denied him a fair opportunity to present his defense. But the
    same failings that render Ulbricht’s expert disclosures inadequate under Rule 16
    preclude us from finding the kind of prejudice he asserts. Ulbricht did not
    disclose to the district court, and has not presented on appeal, any explanation of
    what the proposed experts would have said that would have supported a non-
    speculative basis for doubting the probative value of evidence from a variety of
    electronic and other sources identifying Ulbricht as DPR throughout the life of
    Silk Road. Thus, we cannot conclude that he was prejudiced by the experts’
    exclusion.
    53
    BitTorrent is a peer-to-peer file sharing service that is used to transfer large files
    without disrupting Internet servers. It has both legitimate and illicit purposes. See
    Next Phase Distribution, Inc. v. John Does 1-27, 
    284 F.R.D. 165
    , 167 (S.D.N.Y. 2012).
    95
    C. Curtailing Cross-Examination
    Ulbricht contends that the district court erred in limiting his ability to
    cross-examine two government witnesses: Der-Yeghiayan and Kiernan. “We
    review a trial court’s decision to limit the scope of cross-examination for abuse of
    discretion.” United States v. Cedeno, 
    644 F.3d 79
    , 81 (2d Cir. 2011). “A district court
    is accorded broad discretion in controlling the scope and extent of cross-
    examination.” United States v. James, 
    712 F.3d 79
    , 103 (2d Cir. 2013) (internal
    quotation marks omitted); see Fed. R. Evid. 611(a). Thus, “a district court may
    impose reasonable limits on cross-examination to protect against, e.g.,
    harassment, prejudice, confusion, and waste.” 
    James, 712 F.3d at 103
    (internal
    quotation marks omitted). In general, however, a “district court should afford
    wide latitude to a defendant in a criminal case to cross-examine government
    witnesses.” 
    Id. (internal quotation
    marks omitted). That is so because the
    Confrontation Clause gives “a defendant the right not only to cross-examination,
    but to effective cross-examination.” 
    Id. “[I]t does
    not follow, of course, that the
    Confrontation Clause prevents a trial judge from imposing any limits” on defense
    counsel’s cross-examination of government witnesses. 
    Id. (emphasis in
    original).
    96
    1. Agent Der-Yeghiayan
    Ulbricht argues that the district court erred when it struck portions of Der-
    Yeghiayan’s testimony that referenced his prior belief that Karpeles might be
    Dread Pirate Roberts. Ulbricht also challenges the striking of a similar but
    analytically distinct piece of testimony: Der-Yeghiayan’s statement that
    Karpeles’s attorney had offered information about Silk Road in exchange for
    Karpeles receiving immunity from prosecution. Ulbricht wanted the jury to infer
    that Karpeles had some criminal involvement in Silk Road that motivated him to
    pursue a cooperation agreement with the government.
    Der-Yeghiayan answered the defendant’s initial questions about those
    topics, and the government did not object to them until a later side bar. During
    the side bar, the district court expressed its initial view that the questions were
    proper, but requested written briefing on the subject. After reviewing the parties’
    submissions, the district court agreed with the government that neither Der-
    Yeghiayan’s prior opinions about whether Karpeles was DPR nor Karpeles’s
    offer of information about Silk Road was relevant to Ulbricht’s case. The court
    thus directed the government to identify portions of Der-Yeghiayan’s testimony
    97
    to strike. After the government identified the improper testimony, the district
    court gave a general limiting instruction to the jury:
    You heard testimony while Mr. Der-Yeghiayan was on
    the stand regarding personal beliefs or suspicions he
    may have had about particular individuals at various
    points during his investigation. And I instruct you that
    what the agent suspected about others isn’t evidence
    and should be disregarded. Now, consistent with all of
    the instructions I’m going to give you at the end of the
    case, there was other testimony that Mr. Der-Yeghiayan
    provided which you may consider during your
    deliberations and give it the weight that you deem that
    it deserves. So it’s the suspicions, all right?
    Tr. 974. Ulbricht contends on appeal that the district court erred in striking the
    testimony.
    We disagree. The district court did not err in concluding that Der-
    Yeghiayan’s prior beliefs about Karpeles as a possible DPR suspect were not
    relevant to the charges against Ulbricht. In order to elicit testimony implicating
    an alternative perpetrator, a defendant “must show that his proffered evidence
    on the alleged alternative perpetrator is sufficient, on its own or in combination
    with other evidence in the record, to show a nexus between the crime charged
    and the asserted alternative perpetrator.” Wade v. Mantello, 
    333 F.3d 51
    , 61-62 (2d
    Cir. 2003) (internal quotation marks omitted). Thus, to avoid a “grave risk of jury
    98
    confusion,” a defendant must offer more than “unsupported speculation that
    another person may have done the crime.” 
    Id. at 62
    (internal quotation marks
    omitted). An “agent’s state of mind as the investigation progressed is ordinarily
    of little or no relevance to the question of the defendant[’s] guilt.” United States v.
    Johnson, 
    529 F.3d 493
    , 501 (2d Cir. 2008). Thus, striking Der-Yeghiayan’s
    testimony and instructing the jury to disregard his earlier opinions about
    Karpeles’s possible guilt was not error.54
    Further, any arguable error that occurred was harmless. Defense counsel
    continued to cross-examine Der-Yeghiayan and elicited admissible testimony
    about the earlier investigation into Karpeles; indeed, the district court took over
    cross-examination at several points to assist the defense in asking proper
    questions. Cf. Cotto v. Herbert, 
    331 F.3d 217
    , 254 (2d Cir. 2003) (in considering
    54
    Ulbricht also contends on appeal that the government’s objection to the
    testimony, which occurred at a later sidebar, was untimely. He cites no law in
    support of that argument. In general, an “objection should be made after the
    question has been asked but before an answer has been given.” Hutchinson v.
    Groskin, 
    927 F.2d 722
    , 725 (2d Cir. 1991). That “rule is not inflexible,” 
    id., however, and
    we do not “necessarily find [a]n objection affirmatively waived because it
    might have been interposed a few questions earlier,” United States v.
    Pujana-Mena, 
    949 F.2d 24
    , 33 (2d Cir. 1991). Thus, although a contemporaneous
    objection is preferable, the district court was within its discretion to sustain the
    later objection and strike the testimony.
    99
    whether a Confrontation Clause violation is harmless, we consider, inter alia, “the
    extent of cross-examination otherwise permitted”). Moreover, Ulbricht discussed
    the investigation of Karpeles in his summation without objection. What was
    relevant at trial was any actual evidence pointing to Karpeles as the true Dread
    Pirate Roberts. The district court did not limit Ulbricht’s cross-examination of
    Der-Yeghiayan as to his knowledge of such evidence. The district court directed
    the jury to disregard only testimony as to the agent’s “suspicions,” Tr. 974, a
    subject of “little or no relevance to . . . the defendant[’s] guilt,” 
    Johnson, 529 F.3d at 501
    .
    We similarly reject Ulbricht’s contention that striking Der-Yeghiayan’s
    testimony concerning Karpeles’s offer to provide information about Silk Road in
    exchange for immunity was an abuse of discretion. Absent other evidence in the
    record regarding Karpeles, it was proper to exclude wholly speculative
    suggestions of an alternative perpetrator defense based on Karpeles’s attorney’s
    offer of information in exchange for his client’s immunity. And even assuming,
    arguendo, that the district court erred in striking the testimony, any error was
    harmless. To the extent this testimony was stricken from the trial record, that
    ruling occurred outside the presence of the jury. All the jury was told was to
    100
    disregard testimony about “what the agent suspected about others,” Tr. 974, a
    category that hardly would be understood by the jury to encompass testimony
    about the actions of Karpeles’s attorney. As explained in detail above, moreover,
    the evidence identifying Ulbricht as Dread Pirate Roberts was overwhelming and
    largely unchallenged. That Karpeles may have had information about Silk Road
    does not imply that he was DPR, only that he had some knowledge of or
    involvement with the site. Particularly given that Karpeles likely had some
    knowledge about Silk Road simply because of his operation of Mt. Gox, a
    prominent Bitcoin exchanger, any marginal probative value in the fact that he
    claimed to have such knowledge, and offered to provide it to the government,
    could not have meaningfully affected the balance of evidence available to the jury
    regarding the identity of DPR.
    2. Agent Kiernan
    Defense counsel cross-examined Kiernan extensively, and Ulbricht
    contends on appeal that the district court erred in preventing him from exploring
    certain topics during that cross-examination. Those excluded topics include: the
    101
    meaning of various acronyms, the significance of a certain line of PHP code,55
    whether the FBI allowed Kiernan to run BitTorrent on his work computer despite
    its lack of security, and whether the Linux kernel56 that Kiernan used on his work
    computer was the same as the one that Ulbricht installed on his laptop. Ulbricht
    explains that he was attempting to show that Kiernan’s conclusions about
    Ulbricht’s laptop were inaccurate because they were based on unreliable
    information.
    The district court sustained objections to those questions because, in its
    view, they were outside the scope of Kiernan’s direct testimony. See Fed. R. Evid.
    611(b) (“Cross-examination should not go beyond the subject matter of the direct
    examination and matters affecting the witness’s credibility.”); Baker v. Goldman
    Sachs & Co., 
    669 F.3d 105
    , 110 (2d Cir. 2012) (“Once any direct examination is
    concluded, cross-examination within the scope of the direct follows.”).
    On appeal, Ulbricht claims that, because Kiernan testified about the
    operation of Tor Chat and other forensic computer issues during his direct
    55
    PHP is a common computer programming language that is used primarily in
    website development.
    56
    A kernel is an operating system’s core, and it “is an essential part of the Linux
    operating system.” Tr. 1070.
    102
    testimony, the precluded questions were within that testimony’s scope and
    should have been allowed. Even assuming that Ulbricht is correct, any error is
    harmless. Ulbricht was permitted to question Kiernan about whether Linux was
    customizable, and Kiernan admitted during cross that he did not know whether
    he used the same version of Tor Chat that Ulbricht had installed on his laptop.
    Ulbricht’s counsel also asked several questions about the security vulnerabilities
    of BitTorrent, conveying to the jury that using BitTorrent might have rendered
    Ulbricht’s computer susceptible to hacking. Thus, Ulbricht was able to elicit
    testimony supporting his proposed inference that Kiernan’s conclusions based on
    the Tor Chat evidence were flawed. Ulbricht does not explain how he was
    prejudiced when the district court prohibited him from asking Kiernan certain
    other questions. We therefore identify no reversible error in the district court’s
    limitations on Kiernan’s cross examination.
    D. Andrew Jones Hearsay Statement
    The district court excluded a statement allegedly made by Andrew Jones,
    who was a Silk Road administrator under the username Inigo. Jones cooperated
    with the government and was on the government’s witness list until the middle
    of trial, when the government decided not to call him. Defense counsel explored
    103
    the possibility of calling Jones as a witness, but Jones’s attorney advised Ulbricht
    that Jones would invoke the Fifth Amendment and refuse to testify if compelled
    to appear. In light of Jones’s unavailability, Ulbricht sought to admit a December
    29, 2014 letter from the government to defense counsel that described a statement
    that Jones made during one of his interviews.57 The relevant portion of the
    government’s letter is as follows:
    At some point in or about August or September 2013,
    Jones tried to authenticate that the Silk Road user
    “Dread Pirate Roberts” whom he was talking to at the
    time . . . was the same person with whom he had been
    communicating in the past with this username.
    Previously, . . . Jones and “Dread Pirate Roberts” had
    agreed upon a “handshake” to use for authentication, in
    which Jones would provide a certain prompt and
    “Dread Pirate Roberts” would provide a certain
    response. When, during the 2013 chat in question, Jones
    provided what he believed to be the designated prompt,
    “Dread Pirate Roberts” was unable to provide the
    response Jones thought they had agreed on. However,
    later in the chat, Jones asked “Dread Pirate Roberts” to
    validate himself by specifying the first job that “Dread
    Pirate Roberts” assigned to him (running the “DPR
    Book Club”), which “Dread Pirate Roberts” was able to
    do.
    57
    The government did not concede that the statement was Brady information, but
    disclosed it “in an abundance of caution.” App’x 398.
    104
    App’x 398. Ulbricht argues that the Jones statement58 supports his theory that
    more than one person acted as Dread Pirate Roberts, because at one point DPR
    could authenticate his identity to Jones, but at another time he could not.
    When it became clear that Jones was unavailable to testify, Ulbricht asked
    the government to stipulate that the Jones statement could be read to the jury.
    The government initially agreed, but then changed its mind and opposed
    admitting the Jones statement. The defense acknowledged that the statement was
    hearsay, but claimed that it was admissible under two hearsay exceptions: under
    Rule 804(b)(3), Fed. R. Evid., as a statement against interest, and under Rule 807’s
    residual exception. The district court ruled that the statement was inadmissible,
    specifically addressing only Rule 804(b)(3). On appeal, Ulbricht continues to
    argue that the statement was admissible under either exception. Neither of his
    theories is persuasive.59
    58
    What Ulbricht sought to introduce was the government’s letter paraphrasing a
    statement made by Jones during an interview, not a verbatim transcript of what
    Jones had said. We refer to it as the “Jones statement” for the sake of simplicity.
    59
    We note that the Jones statement is double hearsay, in that the defense sought
    to admit the government’s subsequent characterization of Jones’s interview, and
    both the government’s letter and Jones’s statement to the agents were out of
    court statements offered for their truth. When confronted with “hearsay within
    hearsay, or double hearsay,” courts must determine that “each part of the
    105
    A district court’s “ultimate decisions as to the admission or exclusion of
    evidence are reviewed for abuse of discretion, and will not be disturbed unless
    they are manifestly erroneous.” 
    Davis, 797 F.3d at 201
    (internal quotation marks
    and citations omitted). To invoke the 804(b)(3) exception for a statement against
    interest, the proponent of the statement “must show (1) that the declarant is
    unavailable as a witness, (2) that the statement is sufficiently reliable to warrant
    an inference that a reasonable man in [the declarant’s] position would not have
    made the statement unless he believed it to be true, and (3) that corroborating
    circumstances clearly indicate the trustworthiness of the statement.” United States
    v. Wexler, 
    522 F.3d 194
    , 202 (2d Cir. 2008) (internal quotation marks omitted). The
    exception applies “only if the district court determines that a reasonable person
    in the declarant’s shoes would perceive the statement as detrimental to his or her
    own penal interest.” United States v. Saget, 
    377 F.3d 223
    , 231 (2d Cir. 2004). The
    key to this inquiry is whether the statement is sufficiently “self-inculpatory,”
    combined statement[]” is independently admissible. United States v. Williams, 
    927 F.2d 95
    , 100 (2d Cir. 1991). Because we conclude that no hearsay exception
    applied to the Jones statement at all, we need not address the double hearsay
    issue.
    106
    which the district court must evaluate on a “case-by-case basis.” United States v.
    Williams, 
    506 F.3d 151
    , 155 (2d Cir. 2007).
    The district court did not err in concluding that the Jones statement did not
    fall within Rule 804(b)(3)’s hearsay exception. There is no dispute that Jones was
    unavailable to testify because he planned to invoke his Fifth Amendment
    privilege. The court ruled that the Rule 804(b)(3) exception did not apply because
    Jones was under a cooperation agreement at the time that he made the relevant
    statement to the government and the chat did not have any particular impact on
    Jones’s penal interests. On appeal, Ulbricht claims that the extent of Jones’s
    criminal liability was unknown when he made the statement because he could
    still be vulnerable to prosecution in other jurisdictions, and he had not yet been
    sentenced when he made the statement to the government. See Mitchell v. United
    States, 
    526 U.S. 314
    , 326 (1999) (in the Fifth Amendment context, there can be a
    “legitimate fear of adverse consequences from further testimony” where a
    sentence has not yet been imposed).
    We are not persuaded that Jones’s statement was against his penal
    interests. Given the cooperation agreement, the government’s role at Jones’s
    future sentencing, and the penalties for lying to the government, it is far from
    107
    clear that it was against Jones’s interest to disclose details of his criminal activities
    at the time the statement in question was made. Moreover, even to the extent that
    Jones’s disclosures taken as a whole constituted inculpatory admissions, the
    particular statement in question had little adverse effect on Jones. Jones’s
    inculpatory admissions to the government concern whether he committed crimes
    connected to Silk Road. His description of his “handshake” with DPR
    presupposes that he had already discussed his own crimes with the government.
    Whether DPR did or did not recognize Jones’s identifying prompt does not bear
    on Jones’s guilt of any crime associated with the site, since he had already
    confirmed his role working for DPR. The details of this conversation with DPR
    thus do not inculpate Jones; instead, they either help or hurt Ulbricht.
    Accordingly, the district court did not abuse its discretion in holding that Rule
    804(b)(3) does not apply.
    Rule 807 provides for a limited, residual exception to the rule against
    hearsay where no other exception applies. A hearsay statement may be
    admissible under Rule 807 if: “(i) it is particularly trustworthy; (ii) it bears on a
    material fact; (iii) it is the most probative evidence addressing that fact; (iv) its
    admission is consistent with the rules of evidence and advances the interests of
    108
    justice; and (v) its proffer follows adequate notice to the adverse party.” United
    States v. Morgan, 
    385 F.3d 196
    , 208 (2d Cir. 2004) (internal quotation marks
    omitted). The “residual hearsay exception[] will be used very rarely, and only in
    exceptional circumstances.” Parsons v. Honeywell, Inc., 
    929 F.2d 901
    , 907 (2d Cir.
    1991) (internal quotation marks omitted).
    The district court did not specifically address Ulbricht’s request to admit
    the statement under Rule 807, but we conclude that the limited residual exception
    does not assist Ulbricht. We are loath to assume that a statement made by a
    criminal in debriefings to the government pursuant to a cooperation agreement is
    categorically “particularly trustworthy,” as Rule 807 requires. But even if Jones’s
    statement meets that criterion, and was offered “as evidence of a material fact,”
    we cannot say that it is “more probative on the point for which it is offered than
    any other evidence that the proponent can obtain through reasonable efforts.”
    Fed. R. Evid. 807(a)(2)-(3). Ulbricht has not attempted to explain how the Jones
    statement satisfies this requirement.
    Finally, even if the district court erred in excluding the statement under
    either hearsay exception, any error was certainly harmless. The conversation
    between Jones and DPR in its totality was not actually helpful to Ulbricht. As
    109
    explained, during the chat in question, DPR was at one point unable to provide
    the designated response, but later he identified himself to Jones’s satisfaction.
    The statement thus contains the seeds of its own refutation. Since DPR’s alleged
    failure to verify his identity and his subsequent remedy of that failure occurred
    during the same online chat, the interaction provides little or no support for the
    defense theory that different individuals acted as DPR at different times.
    E. Cumulative Error
    Ulbricht argues that the cumulative effect of the district court’s evidentiary
    rulings deprived him of a fair trial. See United States v. Al-Moayad, 
    545 F.3d 139
    ,
    178 (2d Cir. 2008). We have exhaustively reviewed his contentions of trial error
    and have concluded that none of those contentions has merit. The challenged
    trial rulings were well within the district court’s discretion, and the various
    exclusions did not prevent the defense from offering evidence probative of
    innocence. At the trial in this case, the government presented overwhelming
    evidence that Ulbricht was indeed Dread Pirate Roberts. The evidence that the
    defense was precluded from offering to refute that proof was excluded because it
    was speculative, unreliable, offered in contravention of the Federal Rules of
    Evidence or of Criminal Procedure, or otherwise inadmissible. The few instances
    110
    in which the district court’s rulings may be questioned, where we noted the
    relevance of the harmless error rule, involved minor and marginal points.
    Accordingly, whether considered separately or cumulatively, none of Ulbricht’s
    evidentiary arguments lead us to doubt that he was found guilty after a fair trial.
    III.   Sentencing
    “[A] district court has broad latitude to impose either a Guidelines
    sentence or a non-Guidelines sentence.” 
    Rigas, 583 F.3d at 114
    (internal quotation
    marks omitted). “Accordingly, the role of the Court of Appeals is limited to
    examining a sentence for reasonableness, which is akin to review under an
    ‘abuse-of-discretion’ standard.” 
    Id. “This standard
    applies both to the
    [substantive reasonableness of the] sentence itself and to the procedures
    employed in arriving at the sentence.” 
    Id. (internal quotation
    marks omitted).
    Ulbricht and amici60 challenge his life sentence as both procedurally and
    substantively unreasonable.
    60
    The amici who join Ulbricht’s challenge to his life sentence include: the Drug
    Policy Alliance, Law Enforcement Against Prohibition, JustLeadershipUSA, and
    retired District Judge Nancy Gertner.
    111
    A. Procedural Reasonableness
    “A sentence is procedurally unreasonable if the district court fails to
    calculate (or improperly calculates) the Sentencing Guidelines range, treats the
    Sentencing Guidelines as mandatory, fails to consider the § 3553(a) factors, selects
    a sentence based on clearly erroneous facts, or fails adequately to explain the
    chosen sentence.” United States v. Jesurum, 
    819 F.3d 667
    , 670 (2d Cir. 2016)
    (internal quotation marks and emphasis omitted). To “hold that a factual finding
    is ‘clearly erroneous,’ we must be left with the definite and firm conviction that a
    mistake has been committed.” United States v. DeSilva, 
    613 F.3d 352
    , 356 (2d Cir.
    2010). Where “there are two permissible views of the evidence, the factfinder’s
    choice between them cannot be clearly erroneous.” United States v. Norman, 
    776 F.3d 67
    , 76 (2d Cir. 2015) (internal quotation marks omitted). In general, a
    “sentencing court has discretion to consider a wide range of information in
    arriving at an appropriate sentence.” United States v. Prescott, 
    920 F.2d 139
    , 143
    (2d Cir. 1990). “The district court’s factual findings at sentencing need be
    supported only by a preponderance of the evidence.” 
    Norman, 776 F.3d at 76
    .
    “Where we identify procedural error in a sentence, but the record indicates
    clearly that the district court would have imposed the same sentence in any
    112
    event, the error may be deemed harmless, avoiding the need to vacate the
    sentence and to remand the case for resentencing.” United States v. Jass, 
    569 F.3d 47
    , 68 (2d Cir 2009) (internal quotation marks omitted); see also United States v.
    Cavera, 
    550 F.3d 180
    , 197 (2d Cir. 2008) (en banc) (declining to reach claim that
    district court erred in relying on vague concern about gun violence because it
    was clear that the “district court would have imposed the same sentence had it
    relied solely on” the permissible concern about deterrence).
    Ulbricht’s only claim of procedural error is that it was improper for the
    district court to consider six drug-related deaths as relevant to his sentence
    because there was insufficient information connecting them with drugs
    purchased on Silk Road. In terms of our sentencing jurisprudence, Ulbricht
    claims that the district court relied on clearly erroneous facts in imposing
    sentence. We are not persuaded.
    Ulbricht submitted an expert report in which Dr. Mark Taff wrote that the
    records associated with the six deaths were substantially incomplete. For
    example, many did not include full autopsies, rendering it difficult to discern the
    precise cause of death to a reasonable degree of medical certainty in five of the
    113
    cases.61 Equally importantly, Dr. Taff wrote that he could not conclusively
    connect the specific drugs that the decedents consumed with Silk Road, because
    it is impossible to “correlate the time of purchase/acquisition from an alleged Silk
    Road vendor” and the “time of usage of the alleged Silk road purchase” with the
    deaths.62 S.A. 446. We assume for purposes of this opinion that Dr. Taff’s
    conclusions are sufficiently sound to raise a genuine question about whether the
    deaths described in the PSR were caused by drugs purchased on Silk Road. As
    explained above, however, Ulbricht was not being prosecuted or punished for
    homicide on a theory that he personally caused those deaths. Nor did the fact of
    the deaths increase his offense level under the Guidelines. The question before
    the district court was whether the sale of large quantities of drugs on Silk Road
    61
    In the sixth case, Dr. Taff concluded that the cause of death was ingesting
    multiple drugs coupled with a pre-existing heart condition. The original forensic
    reports concerning that death did not factor in the presence of drugs other than
    synthetic marijuana (obtained via Silk Road) and did not include the heart
    condition as a contributing cause.
    62
    Sentencing amici make a similar argument, claiming that a complex array of
    causes are responsible for drug-related deaths, including societal failures.
    Assuming that is correct, the increased availability of drugs is certainly one of the
    causes of overdose and other drug-related accidental deaths. Thus, the district
    court did not err in concluding that Silk Road, which was by all accounts a
    market-expanding drug enterprise, contributed to the general social costs of drug
    trafficking. Those harms are numerous and include the risk of death.
    114
    created a sufficient risk of death to permit the district court to take the deaths into
    account in assessing the seriousness of Ulbricht’s crimes when it considered the
    factors listed in 18 U.S.C. § 3553(a).
    As with other facts relevant to sentencing, that question is for the district
    court to answer, based on the preponderance of the evidence. 
    Norman, 776 F.3d at 76
    . Contrary to Ulbricht’s claims, the district court did not summarily reject Dr.
    Taff’s conclusions. Rather, it addressed his report carefully and acknowledged
    the evidentiary challenges of connecting the deaths to Silk Road. The court
    concluded that Dr. Taff’s proposed “reasonable degree of medical certainty”
    standard was simply too high an evidentiary standard for purposes of including
    the deaths in the PSR. The court reasoned that it was “not asking whether the but
    for cause of death is drugs purchased on Silk Road,” but rather “whether there is
    a connection between the purchase of drugs on Silk Road and [the] death” in the
    sense that the sale of those drugs created a risk of death. App’x 1476.
    For those limited purposes and judged by that standard, the circumstantial
    evidence connecting the drug-related deaths to Silk Road was sufficient to
    consider them at Ulbricht’s sentencing. To take the strongest example, one
    decedent was found in his apartment with a package torn open. His computer
    115
    had the Silk Road site open, with chat messages from the vendor describing the
    heroin and prescription drug purchase as well as the package tracking
    information. The tracking number matched the information on the torn package
    in the apartment. A toxicology report determined that he died of an overdose of
    heroin combined with other prescription drugs. The facts connecting the other
    five deaths to Silk Road varied in strength. The available evidence was sufficient,
    however, to allow the district court find by a preponderance of the evidence that
    the deaths were connected to Silk Road; therefore, the court could consider the
    risk of death that the site created. Nothing in the sentencing transcript suggests
    that the court considered the information for any other purpose.
    We are sensitive to the possibility that the evidence of the six deaths was
    emotionally inflammatory and risked implicitly escalating Ulbricht’s
    responsibility from facilitating the sale of drugs to causing the deaths of several
    drug users.63 But there is no indication that the deaths in question played such a
    role in the district court’s sentencing determination. In urging the court to
    63
    Ulbricht does not argue that the evidence related to the accidental overdose
    deaths should have been excluded due to its emotional nature; his argument is
    based solely on the claim that the evidence was irrelevant because the deaths
    were not sufficiently linked to Silk Road.
    116
    consider evidence of the deaths, the government explained that the deaths
    “illustrate the obvious: that drugs can cause serious harm, including death.”
    App’x 902. See United States v. Pacheco, 
    489 F.3d 40
    , 48 n.5 (1st Cir. 2007)
    (observing that a defendant who “engaged in the commercial trade of potent
    substances . . . must have known [that such trade] could have dire
    consequences”).
    Of course, to the extent that the harms of the drug trade were obvious,
    there was no need to introduce evidence of these particular incidents, let alone to
    hammer the point home with unavoidably emotional victim impact statements
    by parents of two of the decedents.64 No federal judge needs to be reminded of
    the tragic consequences of the traffic in dangerous substances on the lives of
    users and addicts, or of the risks of overdose and other ramifications of the most
    dangerous of illegal drugs. Those consequences are among the reasons why
    illegal drugs are prohibited and constitute a principal justification advanced for
    the extremely lengthy sentences provided by federal statutes and sentencing
    guidelines for trafficking in illicit substances. Absent reason to believe that a drug
    64
    Ulbricht does not challenge the propriety of those statements apart from his
    general argument that it was procedurally unreasonable to consider the six
    deaths as relevant to his sentence.
    117
    dealer’s methods were unusually reckless, in that they enhanced the risk of death
    from drugs he sold beyond those already inherent in the trade, we do not think
    that the fact that the ever-present risk of tragedy came to fruition in a particular
    instance should enhance those sentences, or that the inability of the government
    to link a particular dealer’s product to a specific death should mitigate them. The
    government’s insistence on proceeding with this evidence generated an appellate
    issue that has taken on a disproportionate focus in relation to the reasons actually
    advanced by the district court in its lengthy and careful statement of the reasons
    for the sentence it imposed. App’x 1509-41.
    We are not persuaded, however, that the introduction of the evidence in
    this case was error, although it may have been incautious for the government to
    insist on presenting it to the district court. As already explained, it was certainly
    appropriate for the district court to consider the risk of death from use of drugs
    in assessing the seriousness of the offense conduct, one of the factors that a judge
    must consider in imposing sentence. See 18 U.S.C. § 3553(a)(2)(A). That appears
    to be the only way the judge in this case used the evidence of the drug-related
    deaths. Emotionally wrenching as the statements of the decedents’ parents were,
    we cannot and do not assume that federal judges are unable to put their
    118
    sympathies for particular victims to one side and assess the evidence for its
    rational relationship to the sentencing decision. And here, the record makes clear
    that the district court did not use the evidence of the drug-related deaths to
    enhance Ulbricht’s sentence, either as a formal matter under the Guidelines or
    otherwise. For all the extensive litigation of the propriety of including this
    information in the PSR, in imposing sentence the district court did not refer to the
    drug-related deaths as an aggravating factor. Indeed, the only mention of that
    evidence at all was a passing reference to “facts brought out in connection with
    [those] death[s]” that “provide evidence of first-time and expanded [drug]
    usage.” App’x 1521-22. This reference occurred in the entirely appropriate
    context of a lengthy discussion of the general social harms of Ulbricht’s massive
    drug-trading marketplace. 
    Id. at 1522-28.
    That discussion was particularly germane to this case for several reasons.
    First, Ulbricht claimed that Silk Road reduced the harms associated with the drug
    trade in several ways. For example, he argued that trafficking in drugs over the
    Internet reduced violence associated with hand-to-hand transactions and the
    societal stigma of drug use, and Silk Road’s vendor rating system ensured that
    customers had access to better quality drugs and more information about the
    119
    drugs that they were purchasing. Those arguments prompted the district court to
    reflect broadly on the costs of the drug trade and discuss Silk Road’s
    participation in those harms. Reasonable people may and do disagree about the
    social utility of harsh sentences for the distribution of controlled substances, or
    even of criminal prohibition of their sale and use at all. It is very possible that, at
    some future point, we will come to regard these policies as tragic mistakes and
    adopt less punitive and more effective methods of reducing the incidence and
    costs of drug use.
    At this point in our history, however, the democratically-elected
    representatives of the people have opted for a policy of prohibition, backed by
    severe punishment. That policy results in the routine incarceration of many
    traffickers for extended periods of time. This case involves a defendant who
    stood at one remove from the trade, who did not for the most part dirty his
    hands with the actual possession and sale of drugs and other contraband that his
    site offered. But he did take a cut of the proceeds, in exchange for making it
    easier for such drugs to be purchased and sold, in a way that may well have
    expanded the market by allowing more people access to drugs in greater
    quantities than might otherwise have been available to them. In the routine
    120
    instances of sentencing drug sellers, the dangerous aspects of the trade are close
    to the surface and require little emphasis. In this case, a reminder of the
    consequences of facilitating such transactions was perhaps more necessary,
    particularly because Ulbricht claimed that his site actually made the drug trade
    safer, and he appeared to contest the legitimacy of the laws he violated.65
    65
    In a footnote in his reply brief, Ulbricht raises for the first time an additional
    argument: that the district court improperly gave him a life sentence because of
    the political and philosophical beliefs that led him to start Silk Road in the first
    instance. Ulbricht argues that reliance on political beliefs at sentencing is
    prohibited by the Guidelines, U.S.S.G. § 5H1.10, and the First Amendment. The
    district court reflected on Ulbricht’s philosophy, however, only in the course of
    discussing his character and his reasons for committing the offense. See 18 U.S.C.
    § 3553(a)(1). That discussion was relevant to sentencing. Ulbricht, as the district
    court concluded,“viewed Silk Road both as above the law and the laws didn’t
    apply.” App’x 1515. He appeared to believe that his personal views about the
    propriety of the drug laws and the paramount role of individual liberty entitled
    him to violate democratically-enacted criminal prohibitions. For example, some
    of his Silk Road posts “discuss the laws as the oppressor” and proclaim that
    “each transaction is a victory over the oppressor.” 
    Id. at 1516.
    That Ulbricht
    believes that drug use should be legalized is not relevant to sentencing; that he
    believes he is entitled to break the laws that prohibit certain substances is
    relevant to his likelihood of recidivism, a mandated sentencing consideration. 18
    U.S.C. § 3553(a)(2)(C). The district court therefore did not sentence Ulbricht based
    on any prohibited characteristic, nor did the court place more weight on that
    factor than the facts warranted. Cf. United States v. Jenkins, —F.3d.—, 
    2017 WL 1371399
    (2d Cir. Apr. 17, 2017) (vacating a sentence as substantively
    unreasonable where the district court relied exclusively on the defendant’s
    “disdain for the law” in “dramatically increasing” a defendant’s sentence for
    child pornography offenses). Ulbricht’s disrespect for the law was simply one
    factor that the district court considered in imposing sentence, along with many
    121
    Finally, we need look no further than the district court’s express reasons
    for imposing sentence to conclude that drug-related deaths played little part in
    dictating the sentence imposed. As tragic as they are, and as foreseeable in light
    of the volume of dangerous drugs trafficked through Silk Road, those deaths
    were accidents. In light of the overwhelming evidence, discussed below, that
    Ulbricht was prepared, like other drug kingpins, to protect his profits by paying
    large sums of money to have individuals who threatened his enterprise
    murdered, it would be plainly wrong to conclude that he was sentenced for
    accidental deaths that the district court discussed only in passing in imposing
    sentence. Even were we to conclude that the evidence of the Silk Road-related
    deaths should not have been received, any error would be harmless, because the
    record is absolutely clear that the district court, after finding that Ulbricht
    commissioned five murders, would have imposed the same sentence if the
    evidence of the drug-related deaths had been excluded.
    The sentencing amici advance one additional argument: that the district
    court’s consideration of the drug-related deaths violated the Fifth and Sixth
    Amendments because the fact of those deaths was not charged in the Indictment
    others, and was not accorded undue weight in determining the sentence.
    122
    and proven to the jury. “While we are not required to address arguments raised
    only by an amicus,” Am. Atheists, Inc. v. Port Auth. of N.Y. & New Jersey, 
    760 F.3d 227
    , 237 n.11 (2d Cir. 2014), we do so here in an excess of caution. The argument
    is without merit under Apprendi v. New Jersey, 
    530 U.S. 466
    (2000), and its
    progeny.
    A district court may consider as part of its sentencing determination
    uncharged conduct proven by a preponderance of the evidence as long as that
    conduct does not increase either the statutory minimum or maximum available
    punishment. See United States v. Stevenson, 
    834 F.3d 80
    , 85 (2d Cir. 2016); United
    States v. Ryan, 
    806 F.3d 691
    , 693-94 (2d Cir. 2015). The Supreme Court has “long
    recognized that broad sentencing discretion, informed by judicial factfinding,
    does not violate the Sixth Amendment.” Alleyne v. United States, 
    133 S. Ct. 2151
    ,
    2163 (2013). Here, the six drug-related deaths (and more importantly, Ulbricht’s
    attempted murders for hire) were uncharged facts that did not increase either the
    statutory twenty-year minimum or the maximum life sentence applicable to the
    crimes of which he was found guilty, beyond a reasonable doubt, by the jury.
    Thus, the district court did not violate the Constitution when it found by a
    preponderance of the evidence that the six deaths were connected to Silk Road
    123
    and that they were relevant to Ulbricht’s sentence because they were part of the
    harm that the site caused.
    In sum, we might not, in the prosecutors’ shoes, have chosen to offer this
    evidence at sentencing, or have admitted it as district judges. We conclude,
    however, (1) that the district court did not clearly err when it found by a
    preponderance of the evidence that the six deaths were connected to Silk Road;
    (2) that it did not abuse its discretion in determining that it was appropriate to
    consider those acts as bearing on the seriousness of the narcotics offenses of
    which Ulbricht was convicted, one of many factors the district court was required
    to consider in exercising its discretion under § 3553(a); and (3) that the evidence
    in question in fact played a minimal role, if any, in the actual sentencing, and that
    in light of the reasons given by the district court for its sentencing decision, we
    can be absolutely certain that the same sentence would have been imposed if the
    evidence had not been received. Ulbricht’s sentence was therefore not
    procedurally unreasonable.
    B. Substantive Unreasonableness
    “We will . . . set aside a district court’s substantive [sentencing]
    determination only in exceptional cases where the trial court’s decision cannot be
    124
    located within the range of permissible decisions.” 
    Cavera, 550 F.3d at 189
    (emphasis and internal quotation marks omitted). Our review is “deferential,”
    and this Court does “not consider what weight we would ourselves have given a
    particular factor.” 
    Rigas, 583 F.3d at 122
    . “Rather, we consider whether the factor,
    as explained by the district court, can bear the weight assigned it under the
    totality of the circumstances in the case.” 
    Id. Our role
    in “patrolling the
    boundaries of reasonableness” is modest. United States v. Broxmeyer, 
    699 F.3d 265
    ,
    289 (2d Cir. 2012) (alterations and internal quotation marks omitted).
    Accordingly, we “will set aside only those outlier sentences that reflect actual
    abuse of a district court’s considerable sentencing discretion.” United States v.
    Messina, 
    806 F.3d 55
    , 66 (2d Cir. 2015).
    In light of the deferential standard of review, we cannot say that Ulbricht’s
    life sentence was substantively unreasonable. The district court identified
    numerous facts that made Ulbricht’s case extraordinary, in its view rendering a
    life sentence “sufficient, but not greater than necessary, to comply with the
    purposes” of sentencing. 18 U.S.C. § 3553(a). The court described the crime as a
    “planned, comprehensive, and deliberate scheme . . . which posed serious danger
    to public health and to our communities.” App’x 1511-12. Silk Road was a
    125
    “worldwide criminal drug enterprise with a massive geographic scope.” 
    Id. at 1512.
    The fact that Ulbricht operated the site from behind a computer, rather than
    in person like a more prototypical drug kingpin, does not make his crime less
    serious or less dangerous. Moreover, Silk Road uniquely expanded the drug
    market by providing an easy avenue for people to become first-time drug users
    and dealers. Because drugs were shipped to customers in the mail, Silk Road
    brought “drugs to communities that previously may have had no access to such
    drugs . . . in such quantities.” 
    Id. at 1522.
    The quantity and nature of the drugs sold on Silk Road are staggering.
    According to the PSR, from 2011 through 2013, Silk Road customers transacted in
    approximately $183 million worth of illegal drugs. At the time the government
    shut down Silk Road on October 2, 2013, there were approximately 13,802 listings
    for controlled substances on the website. Of those listings, there were 643 listings
    for cocaine-based products, 305 for LSD products, and 261 for methamphetamine
    products. The drugs were sold mostly for individual, personal use, but some
    drugs such as heroin and cocaine were also available in “multi-kilogram
    quantities.” PSR ¶ 26. The available drugs were not limited to heroin, narcotics,
    synthetic marijuana, and other dangerous but recreational substances. For
    126
    example, after being told that cyanide was “the most well known assassination
    suicide [sic] poison out there,” Ulbricht allowed vendors to sell it on Silk Road
    despite its singular, deadly purpose. App’x 1519. As the district court noted,
    despite earlier protestations that Silk Road would not allow the sale of products
    that could be used to inflict deliberate harm on others, it took Ulbricht all of six
    minutes to decide “that it is okay to sell cyanide,” 
    id., in exchange
    for the
    customary cut of the proceeds.
    The drug offenses alone—ignoring all other illicit materials sold on the
    site66—yielded a calculated offense level of 50. Of that calculation, only two levels
    66
    As explained, Silk Road also trafficked in illegal goods such as counterfeit
    identification documents and computer hacking tools and services. When the
    government shut down Silk Road, there were 156 listings for forged identity
    documents on the site. The specific computer hacking tools available included
    software for compromising usernames and passwords of electronic accounts,
    including email and Facebook; Remote Access Tools (“RATs”) that allow hackers
    to obtain remote access to a victim’s computer, including turning on and using
    the computer’s webcam; keyloggers, which allow a user to monitor keystrokes
    inputted by a victim to discern their passwords and other sensitive information;
    and Distributed Denial of Service (“DDoS”) tools, which allow hackers to disable
    websites by flooding networks with malicious Internet traffic. Silk Road also
    offered money laundering services through vendors who sold U.S. currency and
    anonymous debit cards. Because the adjusted offense levels for those groups of
    offenses were substantially lower than the offense level for the drug group, they
    did not contribute to Ulbricht’s overall offense level. In assessing the substantive
    reasonableness of the sentence imposed, however, it is well to remember that the
    sentence encompassed Ulbricht’s role not only in the distribution of controlled
    127
    are attributable to Ulbricht’s “credible threats of directed violence” associated
    with the murders for hire. PSR ¶ 94. Thus, even without considering that
    enhancement, the drug convictions yielded an offense level of 48, which is higher
    than the maximum offense level recognized by the Guidelines, for which a
    sentence of life imprisonment is recommended even for someone who, like
    Ulbricht, has no prior criminal convictions. Ulbricht does not challenge the
    accuracy of the Guidelines calculation or of the fact-findings on which it is based.
    That the sentence imposed accorded with the Guidelines recommendation
    does not automatically render it reasonable. See United States v. Dorvee, 
    616 F.3d 174
    , 182 (2d Cir. 2010). The Guidelines are, however, themselves a factor that
    Congress has directed district courts to consider. 18 U.S.C. § 3553(a)(4)(A).
    Moreover, as the considered judgment of the United States Sentencing
    Commission, they bear on the other factors that Congress has required courts to
    evaluate, including the need to reflect the seriousness of the offense, 
    id. § 3553(a)(2)(A),
    to provide adequate deterrence, 
    id. § 3553(a)(2)(B),
    and, because
    they are considered by all judges throughout the federal system, the need to
    substances, but in a wide variety of other criminal offenses as well.
    128
    “avoid unwarranted sentence disparities among defendants with similar records
    who have been found guilty of similar conduct,” 
    id. § 3553(a)(6).
    Accordingly, while a life sentence for selling drugs alone would give
    pause, we would be hard put to find such a sentence beyond the bounds of
    reason for drug crimes of this magnitude.67 But the facts of this case involve much
    more than simply facilitating the sale of narcotics. The district court found by a
    preponderance of the evidence that Ulbricht commissioned at least five murders
    in the course of protecting Silk Road’s anonymity, a finding that Ulbricht does
    not challenge in this appeal.68 Ulbricht discussed those anticipated murders
    callously and casually in his journal and in his communications with the
    67
    Note that such a sentence is mandatory under federal law for selling just five
    kilograms of cocaine after two prior convictions for any felony narcotics offense,
    see 21 U.S.C. § 841(b)(1)(A), and the Supreme Court has upheld against
    constitutional challenge a mandatory sentence of life imprisonment for selling
    650 grams of cocaine, Harmelin v. Michigan, 
    501 U.S. 957
    (1991).
    68
    Ulbricht does not mention his orders for the commission of those murders until
    his reply brief. Even there, he does not argue that the district court erred in
    concluding that he deliberately commissioned those murders; rather, he claims
    instead only that the murders did not support a life sentence because they did
    not actually take place. But in evaluating Ulbricht’s character and dangerousness,
    the most relevant points are that he wanted the murders to be committed, he
    paid for them, and he believed that they had been carried out. The fact that his
    hired assassin may have defrauded him does not reflect positively on Ulbricht’s
    character. Commissioning the murders significantly justified the life sentence.
    129
    purported assassin Redandwhite. For example, in connection with the first hit, he
    wrote to Redandwhite that “FriendlyChemist is a liability and I wouldn’t mind if
    he was executed.” Tr. 1822. In the course of negotiating the price for the killing,
    DPR claimed that “[n]ot long ago, I had a clean hit done for $80k,” 
    id. at 1883,
    but
    that he had “only ever commissioned the one other hit, so I’m still learning this
    market,” 
    id. at 1884.
    He then paid $150,000 in Bitcoins for the murder, and he
    received what purported to be photographic documentation if its completion.
    Ulbricht then wrote in his journal that he “[g]ot word that the blackmailer was
    executed,” 
    id. at 1887,
    before returning quickly to other tasks associated with
    running the site.
    In negotiating the other four killings, Ulbricht initially resisted multiple
    murders. He instructed Redandwhite to “just hit Andrew [usernames Tony76
    and nipplesuckcanuck] and leave it at that.” 
    Id. at 1897.
    Redandwhite said he
    could do it for “150 just like last time,” but that he would not be able to recover
    any of DPR’s money if he killed only one person because he would have to
    commit the murder outside of the victim’s home or office where he stored his
    funds. 
    Id. If Ulbricht
    wanted him to recover money, the self-professed assassin
    claimed, he would have to kill not only Tony76, but also his three associates. DPR
    130
    responded that he would “defer to [Redandwhite’s] better judgment and hope[d]
    [to] recover some assets” from the hit. 
    Id. at 1899.
    He then sent $500,000 in
    Bitcoins, the agreed-upon price for four killings, to Redandwhite. As the district
    court stated in discussing Ulbricht’s journal entries concerning these projected
    murders, his words are “the words of a man who is callous as to the
    consequences or the harm and suffering that [his actions] may cause others.”
    App’x 1521.
    The record was more than sufficient to support the district court’s reliance
    on those attempted murders in sentencing Ulbricht to life in prison. The
    attempted murders for hire separate this case from that of an ordinary drug
    dealer, regardless of the quantity of drugs involved in the offense, and lend
    further support to the district court’s finding that Ulbricht’s conduct and
    character were exceptionally destructive. That he was able to distance himself
    from the actual violence he paid for by using a computer to order the killings is
    not mitigating. Indeed, the cruelty that he displayed in his casual and confident
    negotiations for the hits is unnerving. We thus cannot say that a life sentence was
    outside the “range of permissible decisions” under the circumstances. 
    Cavera, 550 F.3d at 189
    .
    131
    Ulbricht’s arguments on appeal have rhetorical power because of the sheer
    magnitude of his sentence, but they do not provide a legal basis for vacating that
    sentence as substantively unreasonable. He contends that the district court
    ignored the letters submitted on his behalf, thus failing to consider his positive
    contributions to his family and society as well as his potential productivity
    should he be released from prison. To the contrary, however, the district court
    “read each and every one of [the letters] with care,” some “more than once.”
    App’x 1534. Recognizing that the letters were “beautiful” and “profoundly
    moving,” the district court observed that they reveal Ulbricht’s human
    complexity. 
    Id. at 1534-35.
    Nothing in the record supports the claim that the
    district court failed to recognize the importance of the letters, incorrectly
    discounted Ulbricht’s more favorable characteristics, or otherwise
    inappropriately dismissed their role in its sentencing determination.
    Similarly, Ulbricht’s argument that the district court ignored his contention
    that Silk Road reduced the harmful effects of drug crimes must be rejected. The
    district court thoroughly discussed Doctor X’s role at Silk Road and Ulbricht’s
    claims that the site reduced violence, overdoses, and other harms associated with
    drug trafficking, and concluded that they were unpersuasive. We see no error in
    132
    its analysis, and Ulbricht’s arguments concerning harm reduction do not render
    his sentence substantively unreasonable.
    Ulbricht also claims that there is an unwarranted disparity between his
    sentence and the approximately 17-month sentence that Peter Nash, a Silk Road
    administrator, received. Again, however, the district court considered the
    arguments concerning Nash’s sentence and found them to be irrelevant to
    Ulbricht’s crime because Nash was a low-level site administrator who pleaded
    guilty and cooperated with the government. Along those same lines, Ulbricht
    notes that Silk Road drug dealers received lower sentences than he did. For
    example, one such drug dealer received a ten-year sentence. The fact that
    different people involved with the site received dramatically lower sentences
    does not mean that Ulbricht’s own sentence was substantively unreasonable on
    the individual facts of his case.69 Ulbricht was the creator and head administrator
    of the site. That fact alone distinguishes his case from that of any individual seller
    or employee who used or worked for the site. Ulbricht profited from every sale
    69
    In his reply, Ulbricht references other instances in which people involved with
    Silk Road (and its apparent reincarnation, Silk Road 2.0) received significantly
    lower sentences. Ulbricht does not provide sufficient detail about those
    individuals’ conduct, however, to permit meaningful comparisons with his case.
    133
    on Silk Road, and he facilitated the acts of each drug dealer and drug
    organization that used it. Moreover, he attempted to commission at least five
    murders to protect his criminal enterprise. Those facts render his case
    distinguishable from those who committed other crimes using Silk Road or
    otherwise facilitated its operation.
    Ulbricht next reiterates his argument that he was more like someone
    running a crack house than like a drug kingpin because he created the online
    platform that others used to sell drugs and was not himself a drug dealer.70 That
    argument also understates the vast extent of Silk Road’s drug market, which had
    thousands of customers and trafficked in about $183 million in illegal drugs.
    People may differ about whether “respectable” people who, acting as property
    owners, money launderers, or other facilitators of crime for personal gain are less
    guilty than those who personally handle the narcotics. We cannot fault the
    district court for rejecting the argument that Ulbricht’s contribution to the
    narcotics trade was inherently less culpable than that of the dealers who paid him
    to use Silk Road to complete their transactions.
    70
    Ulbricht did sell drugs on Silk Road for at least some brief period of time, when
    he grew and sold hallucinogenic mushrooms to drum up interest in the site.
    134
    Both the sentencing amici and Ulbricht further contend that the district
    court placed too much weight on the notion of general deterrence in meting out
    the life sentence. Specifically, Ulbricht fears that resorting to “general deterrence
    without any confining principles . . . guarantees that [the sentence] will create
    disparity.” Appellant Br. 139. Amici also observe that academic studies counsel
    against placing too much emphasis on general deterrence in sentencing because
    severe criminal punishments do not actually decrease either supply or demand
    for illegal drugs. Further, according to amici, the threat of a long sentence does
    not deter criminal conduct more effectively than the threat of a shorter sentence.
    In his reply, Ulbricht identifies several lucrative dark markets that have emerged
    since Silk Road’s demise in 2013. In his view, the existence of multiple copycat
    Tor-based illegal marketplaces proves that general deterrence is illusory and that
    the district court placed too much weight on that factor.
    Although those arguments have some support among scholars and
    researchers, the ability of a sentence to “afford adequate deterrence to criminal
    conduct” is a factor that district courts are required by Congress to consider in
    arriving at the appropriate sentence. 18 U.S.C. § 3553(a)(2)(B); see United States v.
    Tran, 
    519 F.3d 98
    , 107 (2d Cir. 2008). Congress, moreover, has not concluded that
    135
    the persistence of narcotics crimes is a reason to abandon the efforts to deter
    them by lengthy sentences. The district court observed that “general deterrence
    plays a particularly important role” in Ulbricht’s case because Silk Road is
    “without serious precedent” and generated an unusually large amount of public
    interest. App’x 1532-33. The court thus carefully analyzed the role that general
    deterrence played in Ulbricht’s individual case. At the same time, it is evident
    from the sentencing transcript that general deterrence was “just one element in
    the [district court’s] analysis,” 
    id. at 1533,
    and the district court considered many
    other factors before sentencing Ulbricht to life in prison. Thus, the factor of
    general deterrence, “as explained by the district court, can bear the weight
    assigned it under the totality of circumstances in this case.” 
    Rigas, 583 F.3d at 122
    .
    Finally, Ulbricht and amici point out that life sentences are rare in the
    federal system, typically reserved for egregious violent crimes, thus rendering
    Ulbricht’s sentence substantively unreasonable.71 Moreover, according to amici,
    life sentences are normally imposed in cases where that is the district judge’s
    only sentencing option. Thus, they claim that Ulbricht’s life sentence is
    71
    Amici also claim that Ulbricht’s life sentence violates the Eighth Amendment’s
    ban on cruel and unusual punishment. That argument is plainly incorrect in light
    of binding Supreme Court precedent to the contrary. See Harmelin, 
    501 U.S. 957
    .
    136
    substantively unreasonable in the context of the federal system, where life
    sentences are particularly rare for those with no criminal history who are
    convicted of drug crimes.72
    We agree with Ulbricht that life sentences are extraordinary and
    infrequent, which is as it should be. But the rarity of life sentences does not mean
    that the imposition of such a sentence in this case is substantively unreasonable
    under our law. Each case must be considered on its own facts and in light of all of
    the circumstances of a particular offense as well as other relevant conduct, which,
    in this case, includes five attempted murders for hire. As we have described, the
    district court carefully considered Ulbricht’s offense, his personal characteristics,
    and the context for his crimes, recognizing that only exceptional cases justify
    such a severe sentence. Although we might not have imposed the same sentence
    72
    In his reply, Ulbricht raises a distinct but related argument for the first time. He
    argues that “concurrences from Supreme Court opinions and dissents from
    denials of certiorari suggest[] that judicial factfinding violates a defendant’s
    constitutional right to a jury trial where the factfinding renders reasonable an
    otherwise substantively unreasonable sentence.” Reply Br. 60. For that
    proposition, he cites United States v. Hebert, 
    813 F.3d 551
    , 563 (5th Cir. 2015), cert.
    denied, 
    137 S. Ct. 37
    (2016), Jones v. United States, 
    135 S. Ct. 8
    (2014) (Scalia, J.,
    dissenting from denial of certiorari), and United States v. White, 
    551 F.3d 381
    , 386
    (6th Cir. 2008) (Merritt, J., dissenting). His argument, however, has no support in
    existing law.
    137
    ourselves in the first instance, on the facts of this case a life sentence was “within
    the range of permissible decisions” that the district court could have reached.
    
    Rigas, 583 F.3d at 122
    .
    We do not reach our conclusion lightly.73 A life sentence is the second most
    severe penalty that may be imposed in the federal criminal justice system. “The
    size of [Ulbricht’s] sentence alone [therefore] counsels our careful, searching
    review of it.” United States v. Brown, 
    843 F.3d 74
    , 85 (2d Cir. 2016) (Sack., J.,
    concurring). Courts have the power to condemn a young man to die in prison,
    and judges must exercise that power only in a small number of cases after the
    deepest thought and reflection. Of course, any “sentencing proceeding is a
    solemn occasion at which the judge has the weighty duty of determining the fate
    73
    The life sentence is particularly severe because, as in all federal cases, Ulbricht
    will never be eligible for parole. Unlike state sentences in jurisdictions permitting
    a sentence of, for example, “25 years to life,” there is no automatic
    reconsideration of this sentence, or of whether an offender has reformed, after
    any lengthy period of incarceration. We note that, particularly in the case of a
    young offender, the prisoner will all but certainly change (for better or worse)
    after many years of incarceration. In a system without parole, however, a
    sentencing court is forced to exercise its best judgment to predict whether a
    sentence of life imprisonment or one of 25, 30, or 50 years is required to serve the
    purposes of sentencing, without the option of deferring that judgment to a point
    at which the effects of incarceration, and the passage of time, will be more
    apparent.
    138
    of another human being.” United States v. Alcantara, 
    396 F.3d 189
    , 199 (2d Cir.
    2005). We must be especially sensitive to that duty where the most severe
    sentences are in question. The district court gave Ulbricht’s sentence the
    thorough consideration that it required, reviewing the voluminous sentencing
    submissions, analyzing the factors required by law, and carefully weighing
    Ulbricht’s mitigating arguments. The extraordinarily detailed sentencing
    transcript shows that the district court appreciated its important responsibility in
    considering a sentence of such magnitude and carried out that responsibility with
    care and prudence. Under the law, we cannot say that its decision was
    substantively unreasonable.
    CONCLUSION
    For the foregoing reasons, we AFFIRM the judgment of the district court in
    all respects.
    139
    

Document Info

Docket Number: 15-1815-cr

Citation Numbers: 858 F.3d 71

Filed Date: 5/31/2017

Precedential Status: Precedential

Modified Date: 1/12/2023

Authorities (56)

United States v. Pacheco , 489 F.3d 40 ( 2007 )

United States v. Cavera , 550 F.3d 180 ( 2008 )

In Re Grand Jury Subpoena. John Doe No. 4 v. John Doe No. 1,... , 103 F.3d 234 ( 1996 )

United States v. Charles Williams, Claddis Arrington, Mary ... , 927 F.2d 95 ( 1991 )

United States v. Tran , 519 F.3d 98 ( 2008 )

United States v. Johnson , 529 F.3d 493 ( 2008 )

United States of America, Appellant-Cross-Appellee v. Wendy ... , 385 F.3d 196 ( 2004 )

United States v. Al-Moayad , 545 F.3d 139 ( 2008 )

United States v. Williams , 506 F.3d 151 ( 2007 )

United States v. Rosa , 626 F.3d 56 ( 2010 )

United States v. Wexler , 522 F.3d 194 ( 2008 )

United States v. Mejia , 545 F.3d 179 ( 2008 )

32-fed-r-evid-serv-866-prodliabrepcchp-12792-frank-parsons-v , 929 F.2d 901 ( 1991 )

united-states-v-diomedes-alcantara-also-known-as-lenox-estefan-also , 396 F.3d 189 ( 2005 )

United States v. David Stevens , 985 F.2d 1175 ( 1993 )

United States v. DeSilva , 613 F.3d 352 ( 2010 )

United States v. Philip Prescott , 920 F.2d 139 ( 1990 )

Bonnie J. Hutchinson v. Stephen Groskin, M.D. , 927 F.2d 722 ( 1991 )

United States v. Carmine Avellino , 136 F.3d 249 ( 1998 )

United States v. Cedeno , 644 F.3d 79 ( 2011 )

View All Authorities »