Berger, Jessie v. Iron Wrkr 201 ( 1999 )


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  •                         United States Court of Appeals
    
    
                         FOR THE DISTRICT OF COLUMBIA CIRCUIT
    
    
                 Argued November 30, 1998    Decided March 30, 1999 
    
    
                                     No. 97-7019 
    
                                      "COMPLEX"
    
                               Jessie Berger, et al., 
    
                              Appellees/Cross-Appellants
    
                                          v.
    
                 Iron Workers Reinforced Rodmen, Local 201, et al.,  
    
                              Appellees/Cross-Appellants
    
                 International Association of Bridge, Structural and 
    
                              Ornamental Iron Workers, 
    
                               Appellant/Cross-Appellee
    
                                  Consolidated with 
    
                     Nos. 97-7020;  97-7021;  97-7027; 97-7029; 
    
                                  97-7031 and 97-7124
    
    
                    Appeals from the United States District Court 
    
                            for the District of Columbia 
    
                                     (75cv01743)
    
         Laurence E. Gold and Victor Van Bourg argued the cause 
    for appellants/cross-appellees.  With them on the briefs were 
    Sally M. Tedrow and Ellen O. Boardman.
    
         St. John Barrett argued the cause and filed the briefs for 
    appellants Albert Berger, Alfonzia Berger, and Wordia W. 
    Parks.
    
         John F. Dienelt and John L. Oberdorfer argued the cause 
    for appellees/cross-appellants.  With them on the brief was 
    Christopher L. Killion.  Melvin White, Joseph M. Sellers, 
    James A. Treanor, III, Douglas M. Mangel, Michael R. 
    Goodstein, Jonathan M. Malis, David J. Farber, David G. 
    Leitch, Bonnie H. Rothell, Robert B. Duncan, William C. 
    Edgar, Samuel G. Rubenstein, and Mark E. Martin entered 
    appearances.
    
         Before:  Silberman, Sentelle, and Garland, Circuit 
    Judges.
    
         Opinion for the Court filed Per Curiam.
    
         Concurring opinion filed by Circuit Judge Silberman.
    
         Opinion concurring and dissenting in part filed by Circuit 
    Judge Sentelle.
    
         Opinion concurring and dissenting in part filed by Circuit 
    Judge Garland.
    
         Per Curiam:  This case presents what we hope to be the 
    penultimate chapter in a 23-year-old litigation involving racial 
    discrimination by iron workers' unions against a class of 
    African-American construction workers.  We upheld the un-
    ions' liability a decade ago, and all of the remaining issues in 
    the case concern the remedy due, if any, to those claimants 
    who have thus far not settled with the unions.  Although we 
    are reluctant to prolong this unduly protracted litigation any 
    longer, the district court's failure adequately to resolve the 
    questions presented on appeal compels us to remand many of 
    these challenges to the district court for further factual 
    findings and supporting explanation.  In those instances in 
    which the district court's findings and explanations make it 
    
    
    
    possible for us to resolve an issue definitively, we affirm or 
    reverse the district court's award.
    
                                    I. Background
    
    
         The background of this case is set out in full in our prior 
    opinion, see Berger v. Iron Workers Reinforced Rodmen 
    Local 201, 
    843 F.2d 1395
    , 1405-07 (D.C. Cir. 1988) (Berger I), 
    and we see little need to repeat the details here.  Suffice it to 
    say that in 1975 a class of African-American rodmen--
    construction workers who handle and position steel rods for 
    reinforcing concrete and other building materials--sued Local 
    201 of the Iron Workers Reinforced Rodmen and the Interna-
    tional Association of Bridge, Structural and Ornamental Iron 
    Workers for discriminatorily denying them union membership 
    in violation of Title VII, 42 U.S.C. s 2000e et seq., and 42 
    U.S.C. s 1981.  Rodmen obtained work for construction em-
    ployers in the Washington, D.C. area through referrals dis-
    tributed at Local 201's hiring hall, and although referrals 
    were available to non-union "permit men," priority, along with 
    the other benefits of union membership, went to the union 
    members.  See Berger I, 843 F.2d at 1405.  The class pursued 
    and succeeded on several theories of liability at trial, but we 
    essentially upheld the district court's liability determination 
    on one theory alone.1  We held that the unions were liable for 
    imposing training and apprenticeship prerequisites to taking 
    the journeyman's examination--the entrance examination for 
    union membership.  The class demonstrated with statistical 
    evidence, to which the unions offered no rebuttal, that the 
    educational prerequisites to taking the entrance examination 
    worked to discriminate against "experienced" African-Ameri-
    can rodmen (those rodmen with at least two-years' experience 
    which, according to the class' expert, approximated 2,150 
    rodmen hours).  See Berger I, 843 F.2d at 1414-15.2  We 
    reversed the district court's finding that the unions' various 
    
    __________
         1  We also upheld liability for several individual claims of retalia-
    tion, none of which is relevant in this appeal.
    
         2  We clarified on rehearing that the Apprenticeship Committee 
    and the Training Program, which administered the educational 
    
    
    entrance prerequisites from 1967 to the filing of the suit in 
    1975 constituted a single, continuing pattern of intentional 
    discrimination.  Central to this holding was our conclusion 
    that the so-called "Open Period" from February to June 1971, 
    during which all experienced rodmen were permitted to take 
    the union entrance examination (though a more difficult one), 
    marked a sharp break in the unions' admissions practices.  
    See id. at 1422-23.  We thus limited the liability period to the 
    time between June 1971, the close of the "Open Period" and 
    the beginning of the Training and Apprenticeship prerequi-
    sites, and the filing of the suit on October 21, 1975.  See id. at 
    1422.
    
         Since the trial bifurcated liability and damages, the district 
    court on February 15, 1989, referred the case to a Special 
    Master, Magistrate Patrick J. Attridge, and directed him in 
    an "Order of Reference" to conduct proceedings to calculate 
    the amount of back pay to be awarded to class members and 
    to determine whether class members were entitled to com-
    pensatory and punitive damages and any other relief that 
    might be appropriate.  The Order stated that the class con-
    sisted of the eight named plaintiffs, and any other claimant 
    who could make a prima facie case that he was a member of 
    the class--subject to the unions' rebuttal by clear and con-
    vincing evidence.  It specified the applicable back pay period 
    as follows:
    
         Each individual class member may present a claim for 
         back pay for the period commencing on the date when he 
         first attempted to become, or was deterred or discour-
         aged from becoming, a member of Local 201 and/or the 
         International, and concluding on the date when he first 
         was allowed to take the journeyman examination, pas-
         sage of which is required for membership in Local 201 
    
    __________
    prerequisites, were not jointly liable with Local 201 and the Inter-
    national.  Liability, we said, was established only with respect to 
    the unions' imposition of the requirements themselves, and was not 
    based on the administration of the programs by the Apprenticeship 
    Committee and Training Program.  See Berger v. Iron Workers 
    
    
    
         and the International, or was given a bona fide opportu-
         nity to take the examination.  However, in no event shall 
         the back pay period of any class member commence 
         earlier than October 21, 1972, which is three years prior 
         to the filing of the complaint in this case.
    
    The Order also set forth procedures governing the burdens of 
    proof for establishing the amount of back pay and other relief 
    (prima facie case by claimants subject to the unions' rebuttal 
    by clear and convincing evidence), notice to the class, a 
    schedule for submitting claims, the formula for determining 
    back pay awards, creation of a Relief Account in which the 
    unions would deposit awards for each successful claimant, 
    adjustment of pension records, legal representation of claim-
    ants at individual hearings, and status reports to be filed by 
    the Special Master every six months.
    
         The parties conducted discovery in 1989, and in 1990 the 
    Special Master held individual trials for the 64 remaining 
    claimants3 and heard the parties' respective expert witnesses.  
    By March of 1991, 47 claimants remained, and the parties 
    submitted proposed findings to the Special Master.  Nearly 
    two years later, the class filed a request for a ruling from the 
    district court.  The district court did not respond to this 
    request, nor to a renewed request by the class filed in April 
    1993.  In July 1993, the class sought a writ of mandamus 
    from this court compelling the Special Master to rule, which 
    we denied, expressing confidence (unfortunately unjustified) 
    that the district court would promptly issue a final order 
    resolving all matters covered by the Order of Reference.  
    When the Special Master still had not filed his report by 
    March of 1994 (and thus the district court obviously had not 
    issued a final order either), the class filed a second petition 
    for a writ of mandamus with this court.  Finally, on April 14, 
    1994, three years after the parties submitted proposed find-
    ings, the Special Master issued his report resolving the claims 
    of the 35 remaining claimants.
    __________
    Reinforced Rodmen Local 201, 
    852 F.2d 619
    , 620-21 (D.C. Cir. 
    1988) (Berger II).
    
         3  One hundred and seventy-three claimants participated in the 
    damages phase originally, but many settled their claims and others 
    were excluded for filing untimely claims.
    
    
         In making the class membership determinations, the Spe-
    cial Master defined "experience" on a case-by-case basis, 
    rejecting the unions' contention that 2,150 hours of Local 201 
    rodmen experience was a prerequisite to class membership, 
    as well as their position that a claimant's failure to pass the 
    journeyman's examination is a per se bar to class member-
    ship.  The Special Master concluded that 11 claimants failed 
    to prove membership in the class, and he awarded the 
    remaining 24 claimants back pay, based on a formula multi-
    plying the hourly rodmen wage rate for each year times the 
    difference between the number of hours the claimant actually 
    worked each year as a rodman and the number of hours he 
    would have worked as a union member (less any non-rodwork 
    interim earnings pursuant to 42 U.S.C. s 2000e-5(g)).  The 
    Special Master derived the number representing the average 
    hours a claimant "would have worked"--the so-called "bench-
    mark proxy"--from the pension records of Local 201, and 
    rejected alternative benchmark figures proposed by experts 
    for both the class and the unions.  He also awarded prejudg-
    ment interest at a rate of 6% compounded annually, awarded 
    22 claimants compensatory damages for mental or emotional 
    distress, and denied all of the requests for punitive damages.  
    The parties filed objections to the report, and before the 
    district court could rule, five of the successful claimants and 
    two of the dismissed claimants settled.
    
         We denied the class' second petition for mandamus after 
    the Special Master issued his report in April 1994, and 
    assumed in that order that the district court would act 
    promptly on the report "in light of the long delays in this 
    case."  The district court issued its opinion and order on 
    January 26, 1995.  The court adopted the Special Master's 
    report with respect to the class-wide issues and the awards to 
    the 19 remaining successful claimants, making small correc-
    tions in the amount of the award where appropriate, but 
    specifically noting that its order would not constitute a final, 
    appealable order until the court's subsequent order address-
    ing the excluded claimants' claims issued.  That March 16, 
    1995 order upheld the Special Master's exclusion of the nine 
    remaining claimants from the class, and amended the January 
    
    
    
    26 order by finding clear error, in light of the parties' 1990 
    stipulation to the contrary, in the Special Master's failure to 
    include overtime in the back pay calculations of the successful 
    claimants.
    
         The next two years of this litigation involved premature 
    appeals by the unions and six of the excluded claimants;  
    although the district court indicated in its January 1995 order 
    that the order would become final upon issuance of the March 
    1995 order, the court ordered the plaintiffs to submit pro-
    posed judgment orders and did not certify any of the claims 
    for appeal pursuant to Federal Rule of Civil Procedure 54(b).  
    Accordingly, this court dismissed the unions' appeal pursuant 
    to the class' motion, and dismissed the remainder of the 
    excluded claimants' appeals on its own motion.  The district 
    court entered an order of judgment on January 3, 1997, from 
    which the unions, the class on behalf of the 19 successful 
    claimants, and three excluded claimants, appealed to this 
    court.
    
         The unions challenge a number of legal conclusions and 
    factual findings, both class-wide and with respect to individual 
    claimants, in the district court's opinion (and the Special 
    Master's report that the opinion adopted), including:  the 
    method for calculating the "benchmark proxy" from which 
    individual awards were derived; the standard of review used 
    to determine class membership;  the conclusion that several 
    individuals were properly included in the class;  the calcula-
    tion of several class members' awards;  the conclusion that 
    some class members did not fail to mitigate their damages;  
    and the award of compensatory damages and prejudgment 
    interest.  The class members obviously defend all of those 
    decisions.  In addition, the class argues that the district court 
    erroneously calculated several back pay awards in the unions' 
    favor;  incorrectly concluded that four claimants abandoned 
    their efforts to join the union and forfeited their right to back 
    pay subsequent to their abandonment;  erred by failing to 
    award punitive damages; and should have awarded even more 
    prejudgment interest.  Three individual class members also 
    appeal the district court's decision to exclude them from the 
    class.
    
    
    
                           II. The Benchmark Determination
    
    
         The unions advance numerous arguments against the 
    benchmarks chosen by the Special Master, and the conse-
    quent awards of back pay to the members of the plaintiff 
    class.  We are convinced that the Special Master, and thus 
    the district court, did commit clear error in two respects.  
    The Special Master failed to include "zero-hour" workers 
    (workers who for a number of years worked zero hours as 
    union rodmen) in the determination of the average number of 
    hours worked by a union rodman in the relevant time period, 
    and he failed entirely to address the "fixed-pie" issue raised 
    by the unions' expert, Dr. Farrell Bloch.  First, the zero-hour 
    workers reflect the inherent risk in the work, and failure to 
    adequately account for their absence is clear error.  If the 
    risk of injury is calculated back into the equation when 
    individual back pay awards are determined, it needs to be 
    done explicitly, and the specific experiences of individual 
    rodmen can be measured against the baseline risk of injury to 
    see if they surpass it.  Individual claimants whose injury-time 
    exceeds the statistical average should then be adjusted down-
    ward to reflect the difference between their actual experience 
    and the average.  Second, as we explain below, the fixed-pie 
    analysis permits the court to determine what would have 
    happened in the absence of the discrimination, International 
    Bhd. of Teamsters v. United States, 
    431 U.S. 324
    , 372 (1977), 
    and the burden for showing what those conditions would have 
    been falls on the plaintiff, who is responsible for proving 
    damages.
    
         A.The Special Master's Methodology
    
         We review the findings of fact by the district court, includ-
    ing the findings of the Special Master to the extent that they 
    were adopted by the district court, under a clearly erroneous 
    standard.  See Cuddy v. Carmen, 
    762 F.2d 119
    , 123-24 (D.C. 
    Cir.), cert. denied, 
    474 U.S. 1034
     (1985);  28 U.S.C. 
    s 636(b)(2);  Fed. R. Civ. P. 53(e)(2).  "The findings of a 
    master, to the extent that the court adopts them, shall be 
    considered as the findings of the court."  Fed. R. Civ. P. 52(a).  
    The basic standard for devising back pay awards in a Title 
    
    
    
    VII case is undisputed by the parties.  A court must, "as 
    nearly as possible, recreate the conditions and relationships 
    that would have been, had there been no unlawful discrimina-
    tion," International Bhd. of Teamsters v. United States, 431 
    U.S. at 372 (quoting Franks v. Bowman Transp. Co., 
    424 U.S. 747
    , 769 (1976) (internal quotations omitted)).  The Order of 
    Reference directed the Special Master to determine how 
    many additional hours class members would have worked in 
    the absence of discrimination, and award back pay by multi-
    plying the expected hours worked by the average wage rate 
    in effect during the year that the class member would have 
    worked.  The back pay period began for each individual class 
    member when he was denied access to the examination or 
    deterred from applying for the examination for union mem-
    bership by the educational requirement, and ended when he 
    either took or had a bona fide opportunity to take the 
    entrance examination.  No back pay award could be granted 
    for periods before October 21, 1972, three years before the 
    suit was filed, or after April 10, 1986, when the district court 
    issued its remedial order granting comprehensive injunctive 
    relief.  The amount of back pay awarded to any given mem-
    ber of the plaintiff class is the product of the average wage 
    rate in effect during the time during which the union discrimi-
    nated against him multiplied by the number of hours worked 
    by the average rodman during that time period.
    
         Each side put on expert testimony and presented documen-
    tary evidence sponsoring a method for computing the number 
    of hours worked by the average rodman for purposes of 
    determining the proper amount of a back pay award.  The 
    Special Master noted that one of the primary difficulties with 
    the calculation was the fact that the union did not employ 
    people, but referred them to employers, who individually 
    determined the terms and length of employment.  The Spe-
    cial Master rejected the methods proposed by the expert 
    witnesses in this case, Marc Bendick, Jr. for the claimants 
    and Daniel Quinn Mills and Dr. Bloch for the unions, and 
    created a method of his own based on the documentary 
    evidence in the record.  The Special Master determined that 
    the best proxy for hours worked in the absence of discrimina-
    
    
    
    tion was the hours actually worked by union members during 
    the years in question.  He therefore examined the pension 
    records of Local 201 and calculated how many hours fully 
    employed rodmen worked on average.  The Special Master 
    noted that the "pension records automatically take into ac-
    count the unemployment levels of District of Columbia union 
    rodmen and the average number of days lost due to injury, 
    sickness and attrition."  Report of Special Master, J.A. 341.  
    He explained his choice as follows:
    
              From the Local 201 pension records, a representative 
         group of workers is readily identifiable.  The representa-
         tive group are those workers who received steady refer-
         rals during the relevant time period, as evidenced by a 
         consistent number of hours worked per year.  Workers 
         with consistent referrals worked remarkably similar total 
         numbers of hours for any given year.  Excluded from 
         this group are non-representative workers, i.e., those 
         who for several years during the relevant time period 
         worked no hours at all.
    
              By taking an average of the number of hours worked 
         by those engaged in full time employment and checking 
         that figure for ball-park accuracy against certain indica-
         tors of local iron worker productivity during the relevant 
         time periods, the undersigned arrived at the representa-
         tive or "proxy" number of hours per year that an iron 
         worker could be expected to work.  Based upon these 
         indicia, and taking into account the testimony regarding 
         the relatively recent concept of "double breasting" [in 
         which contractors worked both union and non-union 
         crews], and having also considered all the testimony and 
         exhibits received in evidence, the Special Master finds 
         that the annual hours reasonably expected to be worked 
         by a member of Local 201 is as follows:
    
     
    
          Year    Hours Worked
          1972     1711
          1973     1557
          1974     1627
          1975     1447
          1976     1419
    
    
    
    
         Year    Hours Worked
         1977 1253
         1978 1179
         1979 1230
         1980 1210
         1981 1263
         1982 1168
         1983 1126
         1984   953
         1985 1397
         1986 1549
    See Report of the Special Master at 50-51, J.A. 342-43.  
    Based on his calculations, he arrived at an average of 1,339 
    hours per year.
    
         B.Alleged Errors in the Master's Method
    
         The unions argue that the Special Master committed clear 
    error in the method he adopted for devising a benchmark for 
    purposes of awarding back pay.  Specifically, they argue that 
    he did not sufficiently explain his choice, or show why he 
    failed to adopt the methodology of their expert, Dr. Bloch, 
    which has been endorsed for Title VII remedies in the past.  
    Like the Special Master, Dr. Bloch used a cohort analysis 
    based on pension records, but he used a smaller category of 
    workers, those who were admitted to the union during the 
    period when the union discriminated against the plaintiff 
    class.  Dr. Bloch's calculations also differed from the Special 
    Master's in that they included the zero-hour workers, on the 
    reasoning that a longitudinal analysis of the cohort should 
    incorporate the risk of disabling injury. Finally, Dr. Bloch 
    limited the number of hours that could be awarded with a 
    "fixed-pie" analysis.  He adjusted the benchmark by adding 
    the total number of hours worked by all rodmen, including 
    union members, traveling members from another local, and 
    permit men (non-union workers who were referred to jobs 
    from the union hall).  Members of the plaintiff class, he 
    assumed, would have become union members if the discrimi-
    nation had not occurred, and would have replaced non-union 
    members on jobs that were referred by the union.  In some 
    years, however, there were limited referrals to non-union 
    
    
    members, which Dr. Bloch assumed was due to limited em-
    ployment in the industry generally.  In such years, since only 
    a limited number of hours were available to non-union work-
    ers, class members could not possibly have replaced only non-
    union workers, but would also have displaced other union 
    members.  Reflecting this, the total hours available for such 
    years was placed in a "fixed-pie," and the hours were divided 
    by the total number of union workers plus the number of 
    proven members of the class.  The assumption is that the 
    hours would have been divided equally between all members.  
    See Declaration of Farrell Bloch Ph.D., at 9-11, J.A. 1383-85.
    
         The unions argue that the reason the Special Master gave 
    for rejecting Dr. Bloch's analysis--that the cohort group for 
    1973, consisting of 38 individuals, was a statistically insignifi-
    cant sample--was wrong as a matter of fact and as a matter 
    of law.  The unions point out that Dr. Bloch's proxy group 
    included the aggregate of all 135 journeymen admitted be-
    tween 1971 and 1975, and that the size of the group used by 
    Dr. Bloch exceeds the sample size of union and non-union 
    workers used by the class to establish liability in the first 
    instance.  See Berger, 843 F.2d at 1415.  The unions also 
    argue that the Special Master misunderstood Segar v. Smith, 
    
    738 F.2d 1249
     (D.C. Cir. 1984), which he cited for the proposi-
    tion that the sample was too small.  They distinguish Segar 
    by noting that it applied to a liability decision, not a damages 
    decision.  Further, the Segar panel's analysis took issue with 
    breaking cohorts into smaller and smaller subgroups, until 
    they did become insignificant.  The unions claim that Dr. 
    Bloch's much larger cohort does not resemble those found 
    objectionable in Segar.
    
         The unions cite a line of cases beginning with Pettway v. 
    American Cast Iron Pipe Co., 
    494 F.2d 211
    , 262 (5th Cir. 
    1974), for the proposition that matching the plaintiff class 
    with a comparable group is a favored method of determining 
    what would have happened absent discrimination.  See also 
    Green v. United States Steel Corp., 
    640 F. Supp. 1521
    , 1526-
    29 (E.D.Pa.1986) (calculating damages based on comparable 
    class, and adjusting cohort class for attrition rate), modified 
    
    
    
    on other grounds, Green v. USX Corp., 
    843 F.3d 1511
     (3d Cir. 
    1988), vacated USX Corp. v. Green, 
    490 U.S. 1103
     (1989);  
    Stewart v. General Motors Corp., 
    542 F.2d 445
    , 453-54 (7th 
    Cir. 1976), cert. denied, 
    433 U.S. 919
     (1977) (same).  They 
    also cite a series of cases that have adopted the comparison 
    group methodology in determining Title VII remedies in the 
    construction industry.  See Hameed v. International Ass'n of 
    Bridge, Structural and Ornamental Iron Workers, Local 
    Union No. 396, 
    637 F.2d 506
    , 520-21 (8th Cir. 1980);  Rios v. 
    Enterprise Ass'n Steamfitters Local 638 of U.A., 
    651 F. Supp. 109
    , 111-12 (S.D.N.Y. 1986), modified and remanded, 
    860 F.2d 1168
    , 1177 (2d Cir. 1988).
    
         The class counters that we should adopt the Special Mas-
    ter's analysis, and argues that if he erred, he did so on the 
    low side, because the total he reached, 1,339 hours, was well 
    below the 1,400-hour estimate published by the Institute of 
    Ironworking Industry.  The Special Master as trier of fact 
    was free to accept or reject expert testimony, and was free to 
    draw his own conclusion.  See United States v. Jackson, 
    425 F.2d 574
    , 577 (D.C. Cir. 1970);  Powers v. Bayliner Marine 
    Corp., 
    83 F.3d 789
    , 797-98 (6th Cir. 1996);  Michel v. Total 
    Transp., Inc., 
    957 F.2d 186
    , 192 (5th Cir. 1992);  United 
    States v. 0.161 Acres of Land, 
    837 F.2d 1036
    , 1040-41 (11th 
    Cir. 1988).  The Special Master rejected Bloch's figures be-
    cause his cohort group was too small, and because the Special 
    Master did not credit the fixed-pie theory.  The Special 
    Master found that the union could have found sufficient work 
    for its members, so the pie was not fixed.  The class suggests 
    that this court can recreate the Special Master's results from 
    the record, and should affirm because he cannot be found to 
    have committed clear error.
    
         While we agree that the use of a cohort methodology 
    substantially similar to that used by Dr. Bloch has met with 
    approval in the cases cited by the unions, those cases do not 
    require us to hold that the methodology adopted by the 
    Special Master for defining the cohort to include all union 
    members was clear error.  The cases relied upon by the 
    unions establish neither a specific minimum size of the cohort 
    nor a particular degree of similitude needed to meet the 
    
    
    
    mandates of Title VII.  We therefore hold that rejecting the 
    specific cohort methodology urged by Dr. Bloch was not clear 
    error.
    
         C.Zero-Hour Workers
    
         Nonetheless, the Special Master is required to establish, as 
    nearly as possible, what would have occurred in the absence 
    of discrimination.  International Bhd. of Teamsters, 431 U.S. 
    at 372.  After reading the full report submitted by Dr. Bloch, 
    it becomes clear why he included the zero-hour rodmen in his 
    calculation.  "The mean based on all journeymen including 
    those working zero hours in a given year is appropriate to use 
    in the back pay calculations because it incorporates individual 
    attrition from Local 201 resulting from such factors as tempo-
    rary illness or injury, aversion to rodmen [sic] work, a 
    geographic move away from Local 201's jurisdiction, or the 
    decision to become a contractor."  Report of Dr. Farrell 
    Bloch at 6-7.  Dr. Bloch did not include zero-hour rodmen 
    who had died, retired, were incarcerated or permanently 
    disabled, all conditions which would have limited the unions' 
    liability.  Id. at 7.  The more cursory explanation by the 
    Special Master does not make it clear why he removed the 
    zero-hour workers from the calculation, other than his feeling 
    that they are not representative.  See Report of Special 
    Master at 50.  By removing them from the calculus, the 
    Special Master removes from the equation the risk of disabl-
    ing injury, or of finding another more desirable job, or 
    whatever other reason a person might not work full time.  It 
    is a false assumption that all of the members of the plaintiff 
    class would have remained full time in the industry, given the 
    dangers and disincentives inherent in the work.  The very 
    real risk that they would have been unable or unwilling to 
    continue working has been improperly removed.  The amount 
    an individual would work at full employment should be multi-
    plied by the likelihood that they would remain fully employed.  
    By leaving the zero-hour workers in, Dr. Bloch removed the 
    need for coming up with a figure to approximate that risk.  
    The historic value of that risk is represented by the zero-hour 
    rodmen.  Discounting of this type is a common practice when 
    attempting to fix speculative damages.  The failure to account 
    
    
    for the risks inherent in the industry does amount to clear 
    error.  The Special Master did limit awards where he found 
    that claimants had been disabled for lengthy periods.  How-
    ever, as we explain in Part IV, because there is no quantifica-
    tion of the amount of lost time built into the hours calculation, 
    it is impossible to determine when a claimant is injured for a 
    period that exceeds the anticipated lost time, and the Special 
    Master's inconsistent treatment of claimants when determin-
    ing individual back pay awards shows the need for further 
    analysis on this factual issue.  A specific number can be 
    calculated that quantifies the risk of injury, and then individu-
    als' actual experience should be compared against that figure.
    
         We are not deciding today that each claimant's award must 
    be reduced for excessive injury-time.  It is only because the 
    district court appeared to operate on that assumption, yet 
    applied that assumption without sufficient facts and in an 
    inconsistent manner, that we are compelled to remand these 
    questions.  In this regard, we think it is necessary to note the 
    interrelationship between the inclusion or exclusion of the 
    "zero-hour" workers in the benchmark proxy and the injury-
    time calculation for each claimant.  Both of course are means 
    of discounting back pay awards to reflect unavailability for 
    work during the liability period.  The district court might 
    conclude, if he includes the "zero-hour" workers in the bench-
    mark proxy to reflect the overall risk of injury, that individual 
    re-adjustments for individual claimants with "excessive" 
    injury-time would not be necessary.  In other words, treating 
    all claimants like hypothetically average claimants might obvi-
    ate the need to analyze unavailability for work due to injury 
    for individual claimants.  We do not in any way endorse that 
    outcome, and indeed think the analytical differences between 
    the overall discounting of the proxy caused by inclusion of the 
    "zero-hour" workers and the specific discounting of an indi-
    vidual's award caused by excessive injury-time reductions 
    easily could support doing both.  We wish only to emphasize 
    the interrelationship between these two inquiries, and to 
    direct the district court to consider that relationship when it 
    resolves these issues on remand.
    
    
    
         D."Fixed-Pie" Analysis
    
         We now turn to the Special Master's fixed-pie analysis, and 
    the flawed assumption that underlies it.  The Special Master 
    assumed that the union could have found additional work for 
    its members if it wanted to, had the numbers been increased 
    by admitting the plaintiff class.  See Report of the Special 
    Master at 47-48.  There is no evidence in the record to 
    suggest that there was additional work in the D.C. area for 
    Local 201 rodmen.  In fact, the evidence on the issue of 
    double-breasting suggests that the portion of rodwork avail-
    able to unions generally was declining, as evidenced by the 
    limited work available for permit men.  There is no evidentia-
    ry basis for the assumption made by the Special Master.  
    Common sense and experience suggest that a union will 
    attempt to bring as many projects as possible under union 
    control, and that it will not slow its attempts when the 
    additional work will be allocated to non-members, i.e., permit 
    men, much less when the number of hours available to union 
    members is declining.  Nonetheless, the Special Master cited 
    such a determination on the part of Dr. Bloch as speculative.  
    The Special Master impermissibly switched the burden of 
    proof on this issue.  If the class wished the court to award 
    damages on the basis of hours not referred through the hall, 
    it follows that they would have the burden of at least making 
    a prima facie showing that additional hours were available to 
    Local 201.  Local 201 cannot be faulted for not allocating 
    work that was never brought under its control.  The Special 
    Master placed the burden on the unions to prove that those 
    hours were not available:  "There was no evidence presented 
    that the union would not have solicited other employment 
    opportunities for its members had it been faced with an influx 
    of members, or taken other actions to expand its piece of the 
    rod work 'pie.' "  Report of the Special Master at 47.  The 
    unions made a prima facie showing that the hours were not 
    available based on the declining hours referred out of the hall 
    and the evidence they introduced of the declining market 
    share available to the union due to double-breasting.  As the 
    unions noted in their brief, the record showed that "[t]he 
    percentage of union jobs in the metropolitan Washington D.C. 
    area was 77% in calendar years 1973 and 1974;  peaked at 
    
    
    
    89% in 1975;  and then dropped precipitously to 66% in 1976 
    and 47% in 1977, and then gradually declined to 22% in 1984 
    before rising to 33% in 1986."  Def. Br. at 16.  We remand to 
    the district court to consider the effect of the fixed-pie on the 
    number of hours available to be allocated to the plaintiff class, 
    and to apply the correct burden of proof.  The district court 
    should bear in mind the goal of recreating as nearly as 
    possible the situation that would have occurred in the absence 
    of discrimination.  International Bhd. of Teamsters, 431 U.S. 
    at 372.  That means that it should make findings as to the 
    number of members of the original plaintiff class who actually 
    would have been awarded union membership, and for any 
    given year calculate how many had actually gained member-
    ship, and how many remained to be added into the fixed-pie 
    calculation.  It may well be that the difference by the end of 
    the period is insignificant.  Nonetheless, the failure to consid-
    er the issue, based as it was on the flawed and factually 
    unsupported assumption that additional work was necessarily 
    available to the union, leaves us with no option but to remand.
    
         Judge Garland's dissent takes issue with our holding that 
    the Special Master's failure to consider the "fixed-pie" when 
    calculating damages, and the district court's subsequent adop-
    tion of his report, amounts to clear error.  First, he argues 
    that the unions did not argue that the district court erred in 
    failing to consider this issue.  The unions argued that the 
    district court erred in failing to adopt Dr. Bloch's methodolo-
    gy.  Among the points they enumerate in favor of Dr. Bloch's 
    analysis is the following:  "Once the actual number of claim-
    ants in each year was known, Dr. Bloch would adjust each 
    annual average so that the recalculated claimant hours did 
    not produce a total hours figure for all workers that exceeded 
    the actual total hours worked through Local 201, as derived 
    from the Local 201 pension records."  Def. Br at 28.  While it 
    does not use the specific term "fixed pie," as Judge Garland 
    notes, the argument raised by the unions' brief is the argu-
    ment described by that term.  The fact that the brief argued 
    that all of the methodology used by their expert be adopted 
    does not mean that we may examine either all or none of the 
    points raised.  As we note in our opinion, it is the Special 
    
    
    Master's outright rejection of the issue, based on the unsup-
    ported assumption that the union could have found more jobs 
    if it had so chosen, that we find to be clearly erroneous.
    
         Judge Garland also misconstrues our reasoning with regard 
    to the assumption that the union could bring more rod work 
    under its control if it so chose.  The fact that some 1,649 job 
    requests went unfilled over a 10-year period does not mean 
    that the union had enough work for the 173 putative class 
    members to be fully employed over that same 10-year period. 
    Fluctuations on a given day that would result in a specific job 
    referral being listed as unfilled are not the same as a finding 
    that hundreds of thousands of hours were available.  As we 
    note, the evidence on double-breasting and the steadily de-
    clining share of work available to permit men, annual drop-
    offs of tens of thousands of hours, shows just the opposite.  
    Moreover, the work available, according even to the Special 
    Master's calculations, showed significant disparities over the 
    period.  For instance, in 1972, the average rodman would 
    have worked 1,711 hours, in 1973, 1557 hours, and in 1974, 
    1627 hours.  By 1977, that number had dropped to 1,253 
    hours, and stayed below that level until 1985, bottoming out 
    at 953 hours in 1984.  It makes no sense to conclude a 
    fortiori that a union could readily have found full-time work 
    for 173 additional union members when its existing members 
    were working some 400 fewer hours per year than during the 
    full employment period.  We agree with Judge Garland that 
    it is the gross hours available for referral, not trends, that are 
    relevant to the validity of the fixed-pie theory.  While a more 
    detailed examination of the record, considering such factors 
    as an increasing percentage of class members gaining union 
    membership in the years in question, may once again yield 
    the same conclusion reached below, we cannot affirm, on the 
    record before us, on the basis of the court's stated reasoning, 
    which we find to be clearly erroneous.
    
                                III. Class Membership
    
    
         A.Burden of Proof
    
         We now turn to the issue of the burden of proof at the 
    remedial phase of a Title VII class action suit. Class action 
    
    
    
    lawsuits brought under Title VII are typically bifurcated into 
    two phases, a liability phase and a damages phase, as was 
    done in this case.  The first phase establishes whether the 
    employer is liable to the class because of a pattern or practice 
    of discrimination.  See International Bhd. of Teamsters, 431 
    U.S. at 359.  The second phase addresses questions of class 
    membership and the degree of damage suffered by individual 
    class members.  The district court, in its February 1989 
    Order of Reference, required each claimant to make a prima 
    facie showing of class membership, which could in turn be 
    rebutted by the defendants by "clear and convincing evi-
    dence."  This instruction was in keeping with D.C. Circuit 
    precedent, requiring the defendant to disprove class member-
    ship by clear and convincing evidence at the second phase of a 
    Title VII class-action suit.  See Trout v. Lehman, 
    702 F.2d 1094
    , 1107 (D.C. Cir. 1983), rev'd on other grounds, Lehman 
    v. Trout, 
    465 U.S. 1056
     (1984);  McKenzie v. Sawyer, 
    684 F.2d 62
    , 75-78 (D.C. Cir. 1982).  The unions argue that a super-
    vening Supreme Court case, Price Waterhouse v. Hopkins, 
    
    490 U.S. 228
     (1989), decided weeks after the Order of Refer-
    ence, established that the proper standard of proof in Title 
    VII cases is a preponderance, for both plaintiffs and defen-
    dants.  After careful consideration, we agree.  We review this 
    question of law de novo.  See United States of America v. 
    Perkins, 
    161 F.3d 66
    , 69 (D.C. Cir. 1998).4
    
         The unions acknowledge that Hopkins involved a mixed-
    motives case finding discrimination against an individual, not 
    a disparate-impact class action.  However, they note that "in 
    both situations it remains for a particular individual to prove 
    the defendant's liability to him....  Each claimant is re-
    lieved of the burden of proving that defendants discriminated 
    against the class, not that he is part of the class."  Def. Br. at 
    33.  This is because in the remedial stage of a class action, 
    "as to the individual members of the class, the liability phase 
    
    __________
         4  Because this portion of the panel's decision resolves an appar-
    ent conflict between two of our prior decisions and Price Water-
    house v. Hopkins, it has been separately considered and approved 
    by the full court and thus constitutes the law of the circuit.  See 
    Irons v. Diamond, 
    670 F.2d 265
    , 268 n. 11 (D.C. Cir. 1981).
    
    
    
    of the litigation is not complete."  Hopkins, 490 U.S. at 266 
    (O'Connor, J., concurring).
    
         The class counters that the district court applied the cor-
    rect burden of proof for three reasons.  First, in the damages 
    phase of a class action suit, the defendant is already a proven 
    discriminator, therefore, they argue, increasing the defen-
    dant's burden of proof as to class membership is appropriate.  
    Second, the class argues that the Hopkins case is distinguish-
    able because it was the liability phase of a mixed-motives 
    case, not the damages phase of a class action suit.  Finally, 
    they argue that the unions made no attempt to show a 
    business justification for their testing requirement, and the 
    court is not weighing liability.  Therefore they contend, the 
    court should retain the clear and convincing standard estab-
    lished in McKenzie.
    
         In McKenzie, we read the Supreme Court's precedent as 
    requiring that once the employer was a proven discriminator, 
    " 'all doubts are to be resolved against the proven discrimina-
    tor rather than the innocent employee.' "  McKenzie, 684 
    F.2d at 77 (quoting International Bhd. of Teamsters, 431 U.S. 
    at 372).  We went on to hold that the finding of liability in the 
    first phase of the trial established the prima facie case 
    against the employer, and that the employer "should be 
    required to rebut the plaintiffs' individual showings by clear 
    and convincing evidence."  Id. at 77-78.
    
         Since our holding, the Supreme Court has revisited the 
    issue of the burden of proof in Title VII lawsuits.  In 
    Hopkins, the Court overturned this circuit's holding that an 
    employer in a Title VII sex discrimination case who had 
    allowed a discriminatory motive to play a motivating part in 
    an employment decision was required to show by clear and 
    convincing evidence that it would have reached the same 
    decision in the absence of the discriminatory motivation.  
    Hopkins, 490 U.S. at 238 n.2, reversing Hopkins v. Price 
    Waterhouse, 
    825 F.2d 458
    , 470-71 (D.C. Cir 1987).  The 
    proposition specifically applicable to this case states that no 
    heightened burden is required in Title VII cases, even where 
    a burden shift has occurred.
    
    
    
         Conventional rules of civil litigation generally apply in 
         Title VII cases, and one of these rules is that parties to 
         civil litigation need only prove their case by a preponder-
         ance of the evidence.  Exceptions to this standard are 
         uncommon, and in fact are ordinarily recognized only 
         when the government seeks to take an unusual coercive 
         action--action more dramatic than entering an award of 
         money damages or other conventional relief--against an 
         individual.  Only rarely have we required clear and 
         convincing proof where the action defended against seeks 
         only conventional relief, and we find it significant that in 
         such cases it was the defendant rather than the plaintiff 
         who sought the elevated standard of proof--suggesting 
         that this standard ordinarily serves as a shield rather 
         than, as Hopkins seeks to use it, as a sword.
    
    Hopkins, 490 U.S. at 253 (plurality opinion) (internal citations 
    omitted).  While Justice Brennan was writing for himself and 
    Justices Marshall, Blackmun, and Stevens, Justice White 
    concurred in the judgment "[b]ecause the Court of Appeals 
    required Price Waterhouse to prove by clear and convincing 
    evidence that it would have reached the same employment 
    decision in the absence of improper motive, rather than 
    merely requiring proof by a preponderance of the evidence."  
    Id. at 260.
    
         We think Hopkins mandates that in this case the clear and 
    convincing standard is inappropriate, and the ordinary pre-
    ponderance of the evidence standard must apply.  Hopkins 
    makes it clear that the heightened burden should not apply in 
    Title VII cases where the heightened burden would be used 
    as a sword not a shield.  While this case may not be on all 
    fours with Hopkins, as the distinctions noted by the class 
    demonstrate, the basic principle stated by the Court applies.  
    Raising the burden of proof to clear and convincing evidence 
    is not justified in Title VII cases;  instead a preponderance 
    applies as to all factual issues, regardless of which party 
    bears the burden, as in other civil actions.  The Court relied 
    on the basic principle it articulated--in Title VII cases, the 
    standard burden of proof in civil cases will apply--to decide 
    
    
    Hopkins.  The distinctions to which the class points therefore 
    make no difference to our determination that the preponder-
    ance of the evidence standard, and not a clear and convincing 
    standard, should apply in this case.  The burden shift itself is 
    sufficient to meet the Court's admonition that doubts be 
    resolved in favor of the employee, because the party that 
    bears the burden also bears the risk that he will be unable to 
    carry that burden due to doubts on the part of the factfinder.  
    With these principles firmly in mind, we now go on to 
    consider how that decision affects the facts in this case.
    
         B.Disputed Findings
    
         The district court's adoption of an incorrect standard for 
    the unions' rebuttal burden requires remand of the Special 
    Master's findings of class membership with respect to two 
    claimants, because we are unable to determine whether the 
    Master would have made the same findings if he had applied 
    the correct burden of proof.  In the remaining disputed cases, 
    the validity of the Master's findings turns not on the quantum 
    of the parties' evidence, but on issues that can be resolved 
    without reference to the burden of proof.  Our disposition of 
    the findings disputed by the parties is as follows:
    
         1. O.C. Brown.  The plaintiff class includes those experi-
    enced rodmen who attempted to become, or were deterred or 
    discouraged from becoming, members of Local 201 during the 
    liability period-i.e., between June 1971 and October 21, 1975.  
    See Order of Reference, J.A. 216;  see also Berger I, 843 F.2d 
    at 1411.  Although there was uncontested evidence to support 
    the Special Master's finding that O.C. Brown was "discour-
    aged and deterred from admission" to Local 201, J.A. 86, the 
    conclusion that this occurred during the liability period 
    depends upon disputed inferences from circumstantial evi-
    dence.  Because we are unable to determine whether the 
    Master would have reached the same conclusion had he 
    applied the correct burden of proof, we remand Brown's case 
    for redetermination.
    
         2. Silburn Francis.  There was conflicting testimony and 
    other evidence as to whether Silburn Francis sought union 
    
    
    
    membership during, rather than after, the liability period.  
    See J.A. 400-04.  Because the Special Master weighed this 
    evidence according to an incorrect standard, we remand for 
    redetermination under the correct burden of proof.5
    
         3. John Offer.  The unions do not dispute that John Offer 
    sought union membership in June 1972.  They contend, how-
    ever, that this "predat[es] the critical period," which they 
    define as October 21, 1972 to October 21, 1975.  The unions 
    are mistaken as to the start of the liability period.  October 
    21, 1972 starts the period for which the remedy of back pay is 
    available under 42 U.S.C. s 1981.  See Order of Reference, 
    J.A. 216.  However, as Berger I held, membership in the class 
    is established by having sought (or having been deterred from 
    seeking) entry into the union "from the end of the Open 
    Period [June, 1971] until the filing of suit on October 21, 
    1975"--notwithstanding that back pay may not be awarded 
    for the early part of that period.  See 843 F.2d at 1422.  See 
    generally Thomas v. Denny's, Inc., 
    111 F.3d 1506
    , 1513-14 
    (10th Cir. 1997) (discussing distinction between a liability 
    limitation period, which may effectively be extended by a 
    continuing violation, and "the period within which damages 
    can be recovered," which is fixed by statute).
    
         The unions also contend that Offer was ineligible for the 
    Apprenticeship Program for the "lawful reasons" that he 
    could not meet that Program's educational (high school diplo-
    ma) and age requirements.  However, because Berger I es-
    tablished that the Apprenticeship Program itself was an 
    unlawful prerequisite to union membership for experienced 
    rodmen, see 843 F.2d at 1414, 1421, that Program's own 
    prerequisites are irrelevant.  Offer's membership in the class 
    is affirmed.
    
    __________
         5  In making his determination of the appropriate back pay 
    period for Francis, the Special Master noted that Francis was told 
    he could not apply for membership until he was a U.S. citizen.  J.A. 
    404.  Since discrimination on the basis of citizenship was neither 
    alleged in the lawsuit nor made a part of the liability finding in 
    Berger I, on remand it should play no part in determining Francis' 
    class membership or eligibility for back pay.
    
    
    
         4. Wordia Parks.  Wordia Parks appeals from the Spe-
    cial Master's finding that he abandoned efforts to join Local 
    201 prior to the eligibility period, and that he therefore 
    neither sought nor was discouraged from seeking member-
    ship during that period.  See J.A. 461.  The Special Master 
    also found that Parks' evidence was "inconsistent and contra-
    dictory," and that he had "repeatedly impeached his own 
    responses to interrogatory questions."  J.A. 462.  The Mas-
    ter's findings regarding Parks are not clearly erroneous and 
    therefore are affirmed.
    
         5. Charles Dean and Eldridge Harmon.  To be a mem-
    ber of the class, a claimant must have been an "experienced" 
    rodman.  The unions challenge the Special Master's finding 
    that Charles Dean and Eldridge Harmon were sufficiently 
    experienced, on the ground that the Master counted non-
    union rodwork toward the number of hours required to be 
    regarded as "experienced."  This, the unions contend, is 
    contrary to the "law of the case," because Berger I assertedly 
    established that only union-referred rodwork could be count-
    ed as experience.  We reject this contention because nothing 
    in Berger I limited the definition of experience to union-
    referred rodwork.  See 843 F.2d at 1414-15, 1421-22.
    
         Counting non-union-referred experience, the Special Mas-
    ter accepted the deposition testimony that Charles Dean had 
    the 2,150 hours of experience that all agree is sufficient to 
    establish the necessary experience.  See J.A. 990.  The Mas-
    ter further noted in his report that "by 1974, Dean had 
    performed rodwork for seven years," J.A. 391, which is far in 
    excess of the two-year figure from which the 2,150-hours 
    number was extrapolated.  See Berger I, 843 F.2d at 1414.  
    Because the unions offer no evidence to rebut this prima 
    facie case--no evidence at all that Dean's total hours were 
    less than 2,150--Dean's membership in the class is affirmed.
    
         With regard to Eldridge Harmon, the Special Master ex-
    pressly credited Harmon's testimony that he had worked over 
    2,150 hours by December 1972.  J.A. 407.  Although the 
    unions complain that the Master should have required Har-
    mon to provide documentation to substantiate his testimony, 
    
    
    
    they offer no evidence to rebut Harmon's prima facie case.  
    Accordingly, Harmon's membership is affirmed as well.
    
         6. Alfonzia Berger.  Claimant Alfonzia Berger appeals 
    the Special Master's decision to deny him class membership 
    on the ground that he had no rodwork experience prior to 
    1974.  Although Berger now argues that he was discouraged 
    from seeking the very experience that would have made him a 
    class member, the holding in Berger I was limited to discrimi-
    nation against experienced rodmen.  843 F.3d at 1419.  Al-
    fonzia Berger is not a member of the class of experienced 
    rodmen, and the Special Master's determination is therefore 
    affirmed.
    
         7. Paul Brown, James Hicks, and James Brown.  The 
    unions contend that the Special Master should have excluded 
    from the class two claimants who failed the Open Period 
    exam (Paul Brown and James Hicks), and one claimant who 
    assertedly failed to take that exam despite being given an 
    opportunity to do so (James Brown), because those failures 
    allegedly demonstrate that these claimants were not qualified 
    to be union journeymen.  Berger I, however, made clear that 
    the relevant question is not whether a claimant was qualified 
    during the Open Period, but whether he was qualified during 
    the liability period--which did not begin until the Open 
    Period ended.  The union is liable, we said, "to those class 
    members who were experienced workers, but were delayed 
    entry to union ranks by the particular educational prerequi-
    sites affecting them from the end of the Open Period until the 
    filing of suit on October 21, 1975."  843 F.2d at 1422.  That is 
    the issue upon which the Special Master properly focused.  
    See, e.g., J.A. 383, 412.
    
         Although a failure on the Open Period exam may have 
    rendered a claimant unqualified to enter the union during 
    that period, contrary to Judge Sentelle's dissent it did not by 
    itself render him unqualified to do so during the liability 
    period.  The Local did not have a rule that an applicant who 
    failed the Open Period exam (or any other pre-liability period 
    exam) was ineligible to gain entry by subsequently taking and 
    passing the exam during the liability period.  Indeed, claim-
    ant Hicks was permitted to do just that, and passed the exam 
    
    
    
    in 1974.  J.A. 412.  Failing to pass the exam during the Open 
    Period is no different than having had less than 2,150 hours of 
    rodwork experience during that period.  It may mean a 
    claimant was unqualified to be a journeyman at that time;  it 
    does not mean he could not become qualified by the time of 
    the liability period.
    
         Nor was a failure on the Open Period exam conclusive 
    evidence that a claimant would have failed had he been 
    permitted to take the exam during the liability period.  As we 
    noted in Berger I, the Open Period exam was different from 
    and notably more difficult than the exam offered during the 
    liability period.  During the Open Period, only 70.6% of white 
    examinees and 35.3% of black examinees passed the exam.  
    By contrast, 100% of white rodmen and 97.6% of black 
    rodmen who took the exam given during the liability period 
    passed.  843 F.2d at 1405-06 n.2.
    
         The Special Master's determination of class membership 
    for these claimants is affirmed.
    
         8. Albert Berger.  Finally, claimant Albert Berger ap-
    peals the Special Master's decision to deny him class mem-
    bership on the ground that he failed the exam and then failed 
    to avail himself of an opportunity to retake the exam during 
    the Open Period.  This denial is inconsistent with the Mas-
    ter's correct decision not to exclude the preceding claimants 
    for the same reason.  Berger's failure prior to the liability 
    period neither rendered him unqualified to retake the exam 
    during the liability period, nor indicated he would fail again if 
    permitted to do so.  Indeed, like Hicks, Berger ultimately did 
    retake and pass the exam in 1974.  J.A. 361.  He was not 
    permitted to do so, however, until he completed the Training 
    Program--a requirement we held unlawfully discriminatory 
    in Berger I.  843 F.2d at 1414, 1421.  Accordingly, Albert 
    Berger's exclusion from the class is reversed.
    
                                     IV. Back Pay
    
    
         The unions challenge as clearly erroneous the back pay 
    awards to several class members, contending that the district 
    court failed to deduct from these claimants' awards for cer-
    
    
    
    tain periods of time during which, for one reason or another, 
    they were not entitled to recover back pay.  The class 
    disagrees, but also challenges as clearly erroneous the district 
    court's decision to reduce several other awards for a period of 
    time during which, the class argues, the claimant was entitled 
    to recover.6  We consider each contested claim below.
    
         1. James Brown.  As we noted above, the district court's 
    Order of Reference entitles a claimant to back pay "for the 
    period commencing on the date when [the claimant] first 
    attempted to become, or was deterred or discouraged from 
    becoming, a member of Local 201 and/or the International," 
    such period not to begin prior to October 21, 1972.  The 
    unions contest the $242 back pay award to James Brown in 
    1973 because, according to Brown's own testimony, J.A. 797, 
    Brown first attempted to join the union in 1974.  The class 
    counters that, although Brown's attempt to join the union in 
    1971 predates the applicable liability period, the 1971 attempt 
    gave the unions knowledge, or should have given them knowl-
    edge, that Brown wanted to join the union.  According to the 
    unions, Brown presented no evidence below that he was 
    discouraged from joining the union in 1972 or 1973, and the 
    class does not point to any such evidence in their brief.  The 
    Special Master awarded Brown 1973 back pay without ad-
    dressing this question.  J.A. 375.  In its discussion of class-
    wide issues, the district court approved of the class' knowl-
    edge theory, J.A. 528 n.10, and appeared to agree that it was 
    unnecessary for the Special Master specifically to identify the 
    
    __________
         6  The class asserts that the unions' challenges to the back pay 
    awards are numerically incorrect because the challenges rely on the 
    Special Master's benchmark proxy, which erroneously excluded 
    overtime earnings.  But as the unions concede, the parties stipu-
    lated in 1990 that overtime should be included, and the district 
    court in its March 16, 1995 order concluded that the Special Master 
    erred and ordered the parties to recalculate the back pay figures.  
    J.A. 572.  This presents some confusion since the specific dollar 
    amounts discussed in the briefs are not technically accurate.  We 
    leave it to the district court to calculate the actual amount owed to 
    any claimant consistent with the correct back pay figures, including 
    overtime.
    
    
    
    date on which a claimant first attempted to become a union 
    member, or was discouraged from doing so, since the Special 
    Master implicitly did so when he determined the years of 
    applicable back pay for each claimant.  In its discussion of 
    Brown's award, the district court adopted the Special Mas-
    ter's findings without further comment.  J.A. 547.
    
         We think the 1973 back pay award to James Brown is 
    clearly erroneous.  Despite the district court's apparent ac-
    ceptance of the class' "knowledge" theory, the district court's 
    Order of Reference authorizes back pay only for those claim-
    ants who attempted to join the union, or were discouraged 
    from doing so, within the relevant period--not, as the class 
    would have it, those who did nothing during that period, but 
    whom the union knew or should have known wanted to join 
    because of prior attempts.  Although evidence of discourage-
    ment in joining would be sufficient, the class points to no such 
    evidence as to Brown.  And we think the district court's 
    suggestion that the Special Master implicitly found discour-
    agement from whatever date that he began the back pay 
    award is too much of a stretch, even for deferential review.  
    We note that the district court's resolution of this award is 
    not affected by our instruction to the court on remand to 
    apply the correct burden of proof as to class membership, 
    since the complete absence of evidence supporting Brown's 
    position entitled the unions to prevail even under the more 
    stringent standard.
    
         2. Sherman Johnson.  The unions challenge the 1972 
    award to Sherman Johnson for substantially the same reason 
    that they challenge James Brown's award.  In Johnson's 
    case, however, we affirm the back pay award because the 
    Special Master specifically found that Johnson sought to join 
    the union in 1972.  J.A. 434.  It is true that Johnson testified 
    that he only sought entrance to the union in 1970, 1971, and 
    1973, but the Special Master acknowledged that testimonial 
    omission and pointed instead to Johnson's certification form, 
    which stated that Johnson sought to join in 1972.  J.A. 431 
    n.100.  The unions do not challenge the Special Master's 
    findings on the certification form and thus have waived any 
    
    
    
    objection to it.  We therefore affirm the 1972 award to 
    Johnson, subject of course to any necessary re-calculation if 
    the district court alters the benchmark figures on remand.
    
         3. Robert Posley.  The unions challenge the back pay 
    award to Robert Posley for the portion of 1974 (29%) in which 
    he did not have 2,150 hours of Local 201 union experience.  
    The class' only response is that the Special Master did not err 
    by measuring experience in union and non-union hours.  As 
    we held above, although we agree with the class that experi-
    ence can be measured in union and non-union hours, a 
    showing of 2,150 hours of experience is a prerequisite to class 
    membership.  Because of the Special Master's contrary posi-
    tion on this latter point, we cannot be confident at this 
    juncture that his conclusion that by October 1972 Posley "had 
    been doing iron work for both union and non-union contrac-
    tors for over four years" is consistent with the 2,150 hour 
    prerequisite.  Indeed, the Master said nothing about the 
    number of hours Posley worked at all.  This uncertainty is 
    complicated by the stringent burden of proof that the Special 
    Master erroneously imposed upon the unions to rebut Pos-
    ley's testimony.  We leave it to the district court on remand 
    to decide whether Posley's award for 1974 is consistent with 
    the principles we have outlined in this opinion.
    
         4. Randolph Jackson and Ernest Bellamy.  The district 
    court's Order of Reference directed that a class member's 
    entitlement to back pay ends on "the date when he first was 
    allowed to take the journeyman examination ... or was given 
    a bona fide opportunity to take the examination."  J.A. 216-
    17.  The unions challenge the 1975 back pay award to Ran-
    dolph Jackson to the extent the award postdates Jackson's 
    failure of the exam in March 1975.  The class challenges the 
    back pay award to Ernest Bellamy for the opposite reason;  
    they claim that the Special Master erroneously denied Bella-
    my back pay for the period after September 30, 1974, the 
    date on which Bellamy failed the journeyman's examination.
    
    
    
         We think it obvious that the Special Master's findings, 
    which the district court adopted without comment, are incon-
    sistent.  In discussing Jackson's award, the Special Master 
    awarded Jackson back pay for all of 1975, even though 
    Jackson failed the exam in March of that year.  But in 
    discussing Ernest Bellamy's award, the Special Master cut off 
    back pay after the date on which Bellamy failed the exam, 
    noting the Order of Reference and the fact that there were no 
    challenges to the validity of the examination itself at the 
    merits stage.  J.A. 365 & n.61.  We reconcile the inconsisten-
    cy by reversing the 1975 award to Jackson and affirming the 
    truncated award to Bellamy.
    
         The class' sole argument in support of the contrary result 
    is that the Order of Reference should be read to cut off back 
    pay when a claimant is given a bona fide opportunity to take 
    the exam.  The class reads "bona fide opportunity" to mean 
    "bona fide exam," and argues that neither Jackson's nor 
    Bellamy's exam was a bona fide one.  The class further 
    argues that the Special Master implicitly credited Jackson's 
    contention that Ronnie Vermillion, the union business manag-
    er, was lying when he claimed that Jackson failed the exam in 
    March 1975 because Jackson, an experienced rodmen, did not 
    know the steel tubing sizes.  J.A. 424-25.  In addition, the 
    class contends that the Special Master erroneously excluded 
    evidence that Bellamy intended to use to demonstrate that his 
    exam too was not a bona fide one.
    
         We think the unions are quite correct in contending that 
    these arguments are really challenges to the administration of 
    the journeyman's exam--challenges which were not made at 
    the merits stage and which we cannot, and will not, entertain 
    at this late stage.  The Special Master recognized this point 
    in his discussion of Bellamy's award, and in his discussion of 
    another claimant not part of this appeal, J.A. 398-99, but 
    awarded Jackson a full award because he did not believe that 
    Jackson's exam was bona fide.  Moreover, as the unions point 
    out, this court has repeatedly noted that the Title VII liability 
    of the unions in this case is not related to the journeyman's 
    exam itself or to its administration, but solely to the edu-
    
    
    
    cational prerequisites to taking the examination.  Berger I, 
    843 F.2d at 1440;  Berger II, 852 F.2d at 621.  And although 
    we do not cast doubt on the Special Master's factual finding 
    that Vermillion lied to Jackson about his failure of the exam, 
    the Order of Reference speaks only to the fact of taking the 
    exam, not to the validity of the union's determination that a 
    claimant passed or failed the exam.  And no one contests that 
    Jackson or Bellamy actually took the exam.  Finally, the 
    term "bona fide" in the order of reference clearly modifies the 
    term "opportunity," both of which are set off by a disjunctive 
    from the phrase "allowed to take the ... exam."  The class is 
    thus wrong when it argues that the unions' interpretation 
    would render the term "bona fide opportunity" meaningless.  
    Rather, to accept the class' reading would be to excise 
    "allowed to take the ... exam" from the Order of Reference, 
    converting the remedial inquiry into the altogether distinct 
    liability question of the bona fides of the exam.  For back pay 
    purposes, the inquiry into bona fides in this case is limited to 
    examining, where appropriate, whether a claimant passed up 
    a legitimate opportunity to take the exam.
    
         We therefore affirm this aspect of Bellamy's award7 and 
    reverse the district court's decision to grant Jackson an 
    award for the period following his 1975 failure.  We instruct 
    the district court to reduce Jackson's 1975 award by the 
    appropriate amount, considering of course any alterations to 
    the benchmarks that the court might make on remand.  We 
    note finally that although the district court's error was harm-
    less for 1976, since Jackson was not entitled to any recovery 
    for 1976 under the current benchmark proxy, any alteration 
    of the benchmarks must not result in a 1976 award to Jackson 
    
    __________
         7  The unions also contend that Ernest Bellamy's back pay 
    award for 1972 was erroneously calculated, given that his 1972 tax 
    return listed his earnings at $13,217, whereas the Special Master 
    used Bellamy's social security earning record which listed his 1972 
    earnings as $9,178.75.  The class agrees that the district court 
    clearly erred in the 1972 award.  On remand, Bellamy's 1972 award 
    should be recalculated using the correct 1972 earnings amount.
    
    
    
    given our holding that his entitlement to back pay ended 
    when he took the exam.
    
         5. Eldridge Harmon.  The unions challenge the back pay 
    award to Eldridge Harmon for the years 1985 and 1986 
    because Harmon forewent the opportunity to join Iron Work-
    ers Local 84 in Houston, where Harmon resided from 1976 to 
    1985.  Local 84 is, like Local 201, an affiliate of the Interna-
    tional, and the International's governing constitution provides 
    that a two-year member of any Iron Workers local may 
    obtain a "clearance card" from his local union to apply for a 
    transfer of membership to any other local.  Harmon complet-
    ed Local 84's two-year training program, but did not obtain 
    membership in that union because he failed to pay the 
    initiation fee.  The unions assert that Harmon's back pay 
    awards for 1985 and 1986 are clearly erroneous because 
    Harmon failed to avail himself of the opportunity to become a 
    member of Local 84, which would have enabled him to join 
    Local 201 without having to complete Local 201's discrimina-
    tory prerequisites.  The unions further argue that the Special 
    Master's refusal to accept this argument is inconsistent with 
    his treatment of Edgar James, another claimant who was 
    denied class membership in part because of his failure to avail 
    himself of membership in Local 201 through a "clearance 
    card" procedure.  J.A. 427-30.  The class counters that the 
    unions' argument is highly speculative since the Internation-
    al's governing constitution gives Local 201 the discretion to 
    reject a clearance card from another local union.
    
         We affirm this aspect of Harmon's award.  The Order of 
    Reference only requires back pay termination when a claim-
    ant takes the journeyman's exam, or has a bona fide opportu-
    nity to do so;  it has no provision for terminating back pay in 
    light of a failure to avail oneself of an alternative mechanism 
    for becoming a Local 201 member.  And although it is true 
    that the Special Master discussed Edgar James' failure to 
    take advantage of a "clearance card" procedure to gain 
    entrance to Local 201, that discussion focused on James' 
    inability to prove membership in the class.  James had never 
    attempted to join Local 201, and the Special Master found 
    
    
    
    that James could not have been discouraged from doing so 
    (the alternative means of proving class membership) since 
    James could have joined Local 201 through the "clearance 
    card" procedure.  J.A. 430.  Harmon, on the other hand, is 
    clearly a member of the class because he actually applied for 
    membership in Local 201 and was denied (rendering the 
    discouragement issue irrelevant).  There is thus no inconsis-
    tency between the Special Master's treatment of Harmon and 
    James, and no basis under the Order of Reference to reverse 
    the award to Harmon as clearly erroneous.  This is so even 
    though the unions were subjected to the incorrect clear and 
    convincing evidence standard since, under the more lenient 
    preponderance of the evidence standard, Harmon still would 
    be entitled to his award.
    
         6. Jessie Berger, Silburn Francis, Eldridge Harmon, 
    Thomas Kirkland, and Sherman Johnson.  The unions 
    assert that these five claimants were erroneously given back 
    pay awards for periods during which they had injuries and 
    were unavailable to work.8  The class counters that the 
    benchmark proxy figure already takes into account time off 
    due to minor injuries and bad weather, making it unnecessary 
    to reduce an individual claimant's award for those reasons.  
    For the same reason, the class challenges the Special Mas-
    ter's reduction of Sherman Johnson's award for the one 
    month in 1975 during which Johnson had asthma and could 
    not work.  The district court upheld all of these awards 
    without comment.
    
         The Special Master recognized its obligation in adopting a 
    back pay formula to "as nearly as possible, recreate the 
    
    __________
         8  The unions also claim that, because O.C. Brown testified to 
    his special difficulty in working in cold weather, his back pay award 
    also should be reduced to account for the three-month period in 
    which he was unavailable for work each year.  Unlike the unions' 
    challenges to claimants who had unusually excessive injury-time, we 
    think this challenge to O.C. Brown's award is more appropriately 
    resolved under the duty to mitigate doctrine, which we discuss 
    below.
    
    
    
    conditions and relationships that would have been had there 
    been no unlawful discrimination."  International Bhd. of 
    Teamsters, 431 U.S. at 372.  The Special Master's proxy does, 
    as the class contends, factor in the "average number of days 
    lost due to injury, sickness, and attrition."  J.A. 341.  But the 
    Teamsters obligation arguably requires the district court to 
    modify the benchmark proxy for any claimant whose absen-
    teeism is so extreme as to be beyond the proxy's statistical 
    average.  The Special Master recognized as much in the case 
    of Van Edward Lewis, whose three-year shoulder injury 
    represented an "extensive period of unemployment due to 
    injury [that] falls outside our statistical model of reasonable 
    hours" developed in the benchmark proxy.  J.A. 445.  The 
    problem, however, is that neither the Special Master nor the 
    district court explained the extent to which the "statistical 
    model of reasonable hours" factors in absenteeism due to 
    injuries.  Consequently, the district court had no objective 
    basis on which to determine when a claimant's injury-time 
    was sufficiently excessive to render it beyond the statistical 
    average.
    
         It is not surprising, then, that the analysis below is an ad 
    hoc, internally inconsistent evaluation of the back pay calcula-
    tion for claimants who suffered injuries during the back pay 
    period.  For example, the Special Master reduced Eldridge 
    Harmon's back pay for the one month that he could not work 
    due to a back injury, J.A. 409,9 and reduced Sherman John-
    son's back pay for the one month that he could not work due 
    to an asthma condition.  J.A. 144.  At the same time, the 
    Special Master ignored the evidence relating to Jessie Ber-
    ger's 12-week prostate surgery recovery in 1974, J.A. 367, 
    
    __________
         9  The unions contend, and the class concedes, that the Special 
    Master erroneously stated that Harmon's injury began in Novem-
    ber 1974, when it in fact began on September 28, 1974.  Since the 
    difference between a one-month and a three-month injury might be 
    significant in determining the amount of back pay reduction, if any, 
    we reverse for clear error the district court's finding that Harmon 
    was injured in November of 1974.  Also, the unions are correct that 
    Harmon's interim earnings for 1974 were $10,299, and not $8,316, as 
    the Special Master clearly erroneously found.  J.A. 1501-03;  409.
    
    
    
    ignored evidence relating to Silburn Francis' six-week injury 
    in 1980 after a rod struck him in the stomach, J.A. 405, and 
    ignored evidence of Thomas Kirkland's six-week back injury 
    in 1976, awarding full back pay for the relevant period to each 
    claimant.  Clearly, if a one-month injury warrants a reduc-
    tion, so too must injuries lasting six and twelve weeks.  But 
    we, like the district court, have no objective basis on which to 
    resolve the inconsistency because there has been no finding 
    as to the statistical injury average or how long an injury must 
    last to go beyond that average.10  We therefore remand to the 
    district court for a determination of the average injury-time 
    built into the benchmark figures, and a thorough inquiry into 
    whether each challenged award involves a claimant whose 
    injury-time exceeds that average.
    
         There is one back pay challenge, however, that we can 
    partially resolve now.  The district court awarded Thomas 
    Kirkland a full back pay award for 1976, even though Kirk-
    land stipulated that he was unable to work for the six weeks 
    when he had a back injury and was therefore not asking for 
    back pay for that period.  J.A. 660.  The award is therefore 
    clear error;  we remand for the district court to reduce 
    Kirkland's award to reflect the six-week injury.
    
         7. John Thomas.  The class challenges the district court's 
    denial of back pay to John Thomas for the years 1973 to 1975.  
    The sole basis on which the Special Master and the district 
    court denied back pay for this period was that Thomas' 
    pension records show steady and full-time employment during 
    
    __________
         10  The Special Master also appears to have adopted conflicting 
    methods for reducing back pay because of excessive injury-time.  
    In some instances, he reduced the benchmark proxy for the rele-
    vant period by the percentage of time during which the claimant 
    was unavailable for work, and subtracted the claimant's actual 
    work-time from the reduced benchmark.  See, e.g., J.A. 436 (Sher-
    man Johnson).  However, on other occasions he simply reduced the 
    earnings shortfall (the final back pay award) by the percentage of 
    time during which the claimant was unable to work.  See, e.g., J.A. 
    409-10 (Eldridge Harmon).  On remand, we instruct the district 
    court to apply one method of injury-time reduction consistently, and 
    to explain the basis for picking that method.
    
    
    
    that period.  But the class is correct that steady employment 
    only deprives a claimant of back pay if the earnings from that 
    employment exceed the benchmark earnings for that year.  
    The Special Master did not conduct the necessary analysis, 
    and as the class demonstrates, it appears that Thomas' earn-
    ings for each year between 1972 and 1975 fell short of the 
    benchmark amount.  The unions concede the class' general 
    argument, but argue that the district court did not err by 
    denying Thomas an award for 1973 because Thomas' employ-
    er for that year reported the maximum amount ($10,800) that 
    any single employer was required to report for FICA taxes.  
    The class counters that the question is whether Thomas 
    earned less than the $13,917 benchmark in 1973, which ac-
    cording to their calculations, he did.
    
         The denial of all back pay for 1972-75 years is clear error.  
    We remand Thomas' award for the district court to carry out 
    the analysis and award the appropriate back pay pursuant to 
    the method used to resolve the other claimants' awards.  In 
    this regard, the 1973 award is no different from the 1972, 
    1974, and 1975 awards that the unions concede were errone-
    ously denied to Thomas.  We leave it to the district court to 
    determine whether, as the class contends, Thomas' 1973 
    earnings result in a short-fall entitling him to an award for 
    that year.  This calculation may obviously be affected by any 
    alteration to the benchmark proxy figures on remand.
    
         8. Charles Dean.  The class also argues that the district 
    court's determination that Charles Dean was admitted to 
    Local 201 in January 1981 is clear error;  the record clearly 
    shows he was admitted in January 1982, and the unions 
    concede the class' argument.  If the district court does not 
    alter the benchmarks on remand, or lowers them, this error is 
    of no consequence because Dean's 1981 earnings exceed the 
    current benchmark.  However, if the benchmarks are raised 
    on remand such that Dean would otherwise be entitled to an 
    award for 1981, we instruct the district court not to apply its 
    clearly erroneous finding to deprive Dean of an award.
    
    
    
                                    V. Mitigation
    
    
         The unions challenge many of the Special Master's back 
    pay awards on the ground that the claimants failed to miti-
    gate their damages adequately.  Under Title VII, "[i]nterim 
    earnings or amounts earnable with reasonable diligence by 
    the person or persons discriminated against shall operate to 
    reduce the back pay otherwise allowable."  42 U.S.C. 
    s 2000e-5(g).  This creates a statutory duty to minimize 
    damages on the part of Title VII claimants, which requires 
    them "to use reasonable diligence in finding other suitable 
    employment."  Ford Motor Co. v. EEOC, 
    458 U.S. 219
    , 231 
    (1982).11  The victim of discrimination, however, is "merely 
    required to make 'reasonable efforts' to mitigate his loss of 
    income, and only unjustified refusals to find or accept other 
    employment are penalized under this rule."  Oil, Chem. & 
    Atomic Workers Int'l Union v. NLRB, 
    547 F.2d 575
    , 602 
    (D.C. Cir. 1976).  "[T]he employee is held ... only to reason-
    able exertions in this regard, not the highest standard of 
    diligence."  NLRB v. Madison Courier, Inc., 
    472 F.2d 1307
    , 
    1318 (D.C. Cir. 1972) (Madison Courier I) (internal quota-
    tions and citations omitted).
    
         A claimant "forfeits his right to back pay if he refuses a job 
    substantially equivalent to the one he was denied."  Ford 
    Motor, 458 U.S. at 232.  But "the unemployed or underem-
    ployed claimant need not go into another line of work, accept 
    a demotion or take a demeaning position."  Id. at 231.  Nor is 
    he "required to accept employment at a great distance from 
    his home."  Oil, Chem. & Atomic Workers, 547 F.2d at 604.  
    On the other hand, a claimant may reasonably conclude that 
    he should lower his sights and seek other work, including 
    work outside the industry.  NLRB v. Madison Courier, Inc., 
    
    505 F.2d 391
    , 396 (D.C. Cir. 1974) (Madison Courier II).  
    "The claimant," after all, "cannot afford to stand aside while 
    the wheels of justice grind slowly toward the ultimate resolu-
    
    __________
         11  The back pay provisions of Title VII were modeled on those 
    of the National Labor Relations Act (NLRA), and the Supreme 
    Court has therefore applied principles developed in the NLRA 
    context to Title VII remedies.  See Ford Motor, 458 U.S. at 226 n.8.
    
    
    tion of the lawsuit.  The claimant needs work that will feed a 
    family and restore self-respect."  Ford Motor, 458 U.S. at 
    221.  Indeed, a claimant "may be required ... to 'lower his 
    sights' by seeking less remunerative work after he has unsuc-
    cessfully attempted for a reasonable period of time to locate 
    interim employment comparable with his improperly denied 
    position."  Madison Courier I, 472 F.2d at 1321.
    
         As the above discussion suggests, the elements of the 
    mitigation doctrine can create a dilemma for a claimant.  As 
    we said in Madison Courier I,
    
         If the discriminatee accepts significantly lower paying 
         work too soon after the discrimination in question, he 
         may be subject to a reduction in back pay on the ground 
         that he willfully incurred a loss by accepting an unsuit-
         ably low paying position.  On the other hand ... if he 
         fails to 'lower his sights' after the passage of a reason-
         able period of unsuccessful employment searching, he 
         may be held to have forfeited his right to reimbursement 
         on the ground that he failed to make the requisite effort 
         to mitigate his losses.
    
    Id.  Because of this dilemma, we held that "courts must be 
    careful when applying" the mitigation doctrine, and that "it 
    would not be unreasonable ... to resolve doubts in this area 
    in favor of the innocent discriminatee."  Id.  "[T]he burden of 
    establishing facts in mitigation of the back pay liability" is 
    therefore upon the violator.  Id. at 1318;  accord Oil, Chem. & 
    Atomic Workers, 547 F.2d at 603.
    
         In addressing the unions' mitigation challenges, we are 
    hampered by the Master's failure to address the mitigation 
    question with respect to a number of the challenged claim-
    ants.  Where the Master has been silent, we can uphold an 
    award only if the unions offer nothing to support a claim of 
    non-mitigation other than an inadequate legal theory, and 
    hence fail to satisfy their burden of proving non-mitigation.
    
                                          A.
    
    
         We begin with four claimants whom the unions contend 
    "did not consistently seek Local 201 referrals" between 1972 
    
    
    and 1975, when there was a surfeit of work available through 
    the Local.  Def. Br. at 54.  Because the Local had more than 
    enough work during this time for any permit man who 
    wanted it, the unions contend that a failure to seek referrals 
    from the union constituted a failure to mitigate.  See id. at 
    54-55, 59-60.
    
         1. O.C. Brown.  Surprisingly, the first claimant the un-
    ions offer as an example of one who failed to seek referrals 
    from the Local is O.C. Brown, who the unions concede did 
    seek and receive many referrals between 1972 and 1978.  Id. 
    at 56.  The problem with Brown, the unions assert, is that he 
    held few of those referred jobs for very long because of his 
    "chronic, voluntary, premature quits," and that as a result his 
    yearly work hours were low.  Id. at 57.  The Special Master, 
    however, credited Brown's testimony on the subject and 
    found that the reason for those "quits" was that "even when 
    referred, Brown was fired on instructions from the business 
    agent [for the union] solely because of his status as a permit 
    man...."  J.A. 382.  The unions cite only one specific exam-
    ple of a "quit," Brown's decision to leave a job at Wahib Steel 
    because of a dispute with a foreman.  But the Master found 
    that "Brown was not unemployed after quitting Wahib but 
    appears to have immediately obtained employment" from 
    another employer.  J.A. 381.  Accordingly, the Master con-
    cluded that no deduction from Brown's back pay award was 
    required, and we cannot find that conclusion clearly errone-
    ous.
    
         As noted in Part IV above, however, the unions have 
    asserted another ground for deduction in Brown's case:  that 
    Brown voluntarily absented himself from the workforce every 
    winter.  There is evidence in the record to support this 
    assertion.  See J.A. 772-75.  Although there may be reasons 
    why such absences do not constitute a failure to mitigate (e.g., 
    because little rodwork was done in the winter, a point made 
    by the unions' own expert, see J.A. 332), the Master did not 
    address Brown's seasonal absences at all, and we therefore 
    must remand his award for further consideration.12
    
    __________
         12  On remand, the district court should also consider the unions' 
    contention that Brown failed to mitigate during the period 1975-78.  
    
    
    
         2. Silburn Francis.  The second claimant the unions 
    challenge for not seeking Local 201 referrals is, again, a 
    claimant who the unions concede did seek and receive refer-
    rals from the union.  Moreover, the unions concede that 
    Silburn Francis, unlike O.C. Brown, "worked high numbers of 
    hours through Local 201 between January 1, 1971 and June 
    30, 1974."  Def. Br. at 57.  Nonetheless, the unions contend 
    that Francis "achieved those hours only by working an unusu-
    ally high number of different jobs," and thus was "a chroni-
    cally lackadaisical worker" who could not hold a job.  Id. at 
    56-57.  Once again, the Special Master drew a different 
    conclusion from the same testimony and documentary record.  
    The Master read Francis' employment history not as indicat-
    ing that he was "lackadaisical," but as "demonstrat[ing] Fran-
    cis' tenacity in seeking work as an ironworker."  J.A. 405.  
    Francis, the Master found, "made good faith and diligent 
    efforts to obtain employment through references from Local 
    201."  J.A. 405.  That finding is not clearly erroneous.13
    
         3. Eldridge Harmon and James Hicks.  Although El-
    dridge Harmon did seek referrals from the union, he mostly 
    worked on non-union jobs.  Similarly, James Hicks worked 
    for a number of non-rodwork employers.  Because there was 
    more than enough union rodwork available during this period, 
    and because that work presumably paid higher wages,14 the 
    unions contend that claimants' failure to seek solely Local 201 
    work during this period constituted a failure to reasonably 
    mitigate.  They were "not available for Local 201 referrals," 
    the unions contend, when they were "working elsewhere."  
    Def. Br. at 60.
    
    __________
    The unions cite evidence that Brown never sought employment 
    from a specific company he believed would have hired him, see Def. 
    Br. at 64, notwithstanding that he worked few hours during that 
    period, see J.A. 379-80.
    
         13  Francis' award is subject, however, to the outcome of the 
    remand of his class membership, as discussed in Part III.B.2 above.
    
         14  This appears to be the unstated (and undisputed) premise of 
    the unions' argument.
    
    
    
         Whether the decisions of these claimants not to seek work 
    solely through the Local constituted a failure to mitigate 
    depends on the reasons they had for taking other work.  As 
    we noted in Oil, Chemical & Atomic Workers, it may be 
    reasonable for a claimant to decline an interim job from his 
    employer (other, of course, than the very job at issue in his 
    lawsuit) in favor of a lower-paying but more permanent job 
    from someone else.  547 F.2d at 604-05.  A fortiori, it may 
    be reasonable to decline to leave an existing job when doing 
    so would only make oneself available for possible referral to a 
    better-paid one.  We do not know whether these kinds of 
    considerations explain Harmon's or Hicks' decisions, however, 
    because the Special Master did not discuss mitigation with 
    respect to Harmon or Hicks at all.  Accordingly we have no 
    choice but to remand their awards for further consideration.
    
                                          B.
    
    
         The unions next address the post-1975 period, which saw 
    employment patterns in the rodwork industry fluctuate.  
    "Even during this period," the unions argue, "Local 201-
    referral jobs went unfilled for lack of applicants."  Def. Br. at 
    60.  The unions therefore again contend that a claimant did 
    not reasonably mitigate if he did not seek work through Local 
    201.  In a set of further, sometimes contradictory arguments, 
    however, the unions contend that a claimant did not reason-
    ably mitigate if he did not also seek union rodwork in other 
    cities, seek non-union rodwork, seek other construction work, 
    and register with government employment agencies.  We 
    consider these individual challenges below.
    
         1. James Brown.  The unions do not dispute that James 
    Brown sought and received referrals from Local 201.  In a 
    one-sentence challenge to Brown's award, however, they ar-
    gue that he "did not seek work through any other Iron 
    Workers Local union or through any other union during 1975 
    and 1976."  Id. at 63.  That argument is insufficient to satisfy 
    the unions' burden.  First, this kind of challenge to Brown's 
    1975 award directly contradicts the unions' argument--dis-
    cussed in Part V.A above--that because Local 201 had more 
    
    
    
    than enough work for permit men from 1972-75, a claimant's 
    failure to seek work solely through Local 201 during that 
    period constituted a failure to mitigate.15  Nor do the unions 
    offer evidence that in 1976 Brown would have had a better 
    chance of obtaining union work in other cities than by con-
    tinuing to seek referrals from Local 201.  Since, as the 
    Master noted, Brown's strategy of seeking work through 
    Local 201 earned him nearly as much or more than the 
    benchmark wages in 1972-74, J.A. 375, and since the unions 
    concede "Local 201-referral jobs went unfilled for lack of 
    applicants" even during the post-1975 period, Def. Br. at 60, 
    the unions' single-sentence challenge does not meet their 
    burden of showing that Brown was unreasonable in continu-
    ing to seek work through Local 201.  Brown's awards are 
    affirmed.
    
         2. Sherman Johnson.  The unions contend that Johnson 
    should not have been awarded back pay for 1975 because he 
    sought no work from non-union companies, non-Local 201 
    unions, or non-rodwork employment during that year.  Once 
    again, this directly contradicts their contention that 1975 was 
    a "full employment" year at Local 201, with plenty of work 
    for any permit man who wanted it, and consequently that any 
    
    __________
         15  See Def. Br. at 54-55, 59-60.  As noted above, the unions 
    contended that a claimant failed to mitigate if he took jobs with 
    non-union employers during this period, thus making him "not 
    available for Local 201 referrals when he was working elsewhere." 
    Id. at 60.  The unions further contended that:
    
         Local 201 was unable to fulfill employer requests that it 
         dispatch workers for 4,432 jobs during the period 1972-75....  
         Local 201 fell short of supplying workers only because it 
         exhausted the rodmen who were available to be referred on all 
         classes on its list.  And, during pension years 1973 to 1976, 
         union members were only able to work 36%, 32%, 35% and 48% 
         respectively, of the hours worked by all workers referred by 
         Local 201.  At least during this period, then, a claimant would 
         exercise reasonable diligence only by consistently seeking em-
         ployment through Local 201, just as the union's member did.
    
    Id. at 55.
    
    
    claimant who did not seek work solely through Local 201 
    failed to mitigate.  The award is affirmed.
    
         3. Charles Dean.  The unions argue that Charles Dean 
    failed to mitigate because he never applied to the leading non-
    union employer, Miller & Long, during the 1975-79 period.  
    The unions, concede, however, that Dean did work for other 
    non-union firms, id. at 64, and offer no evidence that Dean 
    could have done better at Miller & Long.  Indeed, the Master 
    found that Dean's actual hours during this period approached 
    or exceeded the benchmark figures in all relevant years.  
    Accordingly, the unions cannot meet their burden of showing 
    a failure to reasonably mitigate.  The awards are affirmed.
    
         4. Van Edward Lewis.  The unions challenge Lewis' 
    awards for 1977 and 1979, claiming that he ceased seeking 
    work through Local 201 in 1976 and did not return to the 
    union until 1980.  The unions offer no evidence, however, that 
    supports this claim.  The portion of Lewis' testimony cited in 
    support says that he ceased trying to "join the training 
    program" in 1976, not that he ceased seeking permit man 
    work through Local 201.  See Def. Br. at 65 (citing J.A. 736).  
    The Master's report does suggest that Lewis may not have 
    sought Local 201 work in 1979, but that is only because it 
    shows he worked for Miller & Long during that year--the 
    same non-union employer from which the unions insist 
    Charles Dean should have gotten his work.  Accordingly, the 
    awards are affirmed.
    
         5. Thomas Kirkland.  Citing a less-than-clear portion of 
    Kirkland's testimony, the unions contend that he voluntarily 
    ceased looking for work during the last quarter of 1976 and 
    hence failed to mitigate during that period.  The Master did 
    not address this issue at all, and we therefore remand this 
    portion of Kirkland's award for reconsideration.
    
         6. John Offer.  The unions challenge Offer's awards for 
    1975 and 1976, on the ground that he did not seek in-town 
    work from non-union rod companies, or out-of-town work 
    from union companies.  The challenge to the 1975 award fails 
    for the same reason it failed in the cases of James Brown and 
    Sherman Johnson.  We must remand the 1976 award, howev-
    
    
    
    er, because the Special Master failed to discuss the mitigation 
    issue despite claimant's low earnings that year.
    
         7. John Thomas.  The unions challenge Thomas' awards 
    for 1976, 1977 and 1979 on the basis of his asserted failure to 
    adequately mitigate.  With respect to 1976, they contend that 
    he principally collected unemployment compensation rather 
    than working.  Because Thomas earned only $338 in that 
    year, and because the Master did not address the mitigation 
    issue for that year at all, we remand the 1976 award.  With 
    respect to the remaining two years, however, the Master 
    noted that Thomas earned approximately 80% of the bench-
    mark figure in 1977 (by working for Miller & Long) and 98% 
    of the benchmark figure in 1979.  J.A. 480.  These figures 
    suggest reasonable mitigation in those years, and because the 
    unions offer no evidence that Thomas could have done better 
    by seeking any other kind of employment, we affirm those 
    awards.
    
         8. Ronald Tucker.  The unions challenge the awards of 
    back pay to Tucker for 1975 and 1977, on the ground that he 
    did not seek work through any union other than Local 201 or 
    register with an employment agency.  The challenge with 
    respect to 1975 fails for the same reason it failed in the case 
    of the other claimants' 1975 awards.  With respect to 1977, 
    the Master awarded back pay to Tucker for only one calendar 
    quarter and noted that during that entire quarter Tucker 
    worked for a steel company in Baltimore.  The unions have 
    proffered no evidence that other work would have paid more, 
    or that Tucker's mitigation efforts were otherwise unreason-
    able.  They are thus unable to satisfy their burden of showing 
    a failure to mitigate.  The awards are affirmed.
    
                                          C.
    
    
         Finally, we also consider the class' challenges to the Special 
    Master's decision to truncate the awards of four claimants on 
    the ground that after certain dates those claimants "aban-
    doned" Local 201.  We remand two of those decisions, and 
    affirm the other two.
    
    
    
         1. James Brown and Ronald Tucker.  The Special Mas-
    ter cut off Brown's and Tucker's back pay awards after 1976 
    and 1977, respectively, because they obtained non-union em-
    ployment and ceased to seek union referrals.  J.A. 376, 483.  
    We agree with the unions that this issue is properly evaluated 
    by applying the mitigation doctrines described above.  See 
    Def. Reply Br. at 6, 13-14.  But the Master's decision to 
    truncate the awards solely because the claimants chose to 
    keep working at alternative employment, rather than con-
    stantly to seek new union referrals, misapplies those doc-
    trines and requires a remand.
    
         To infer a breach of the duty to mitigate solely from a 
    claimant's acceptance of other work implicates the dilemma 
    noted at the beginning of this Part, and creates a Catch-22 
    situation for the claimant.  As the Third Circuit has said:
    
         [T]he fact that a plaintiff takes a job in an unrelated field 
         to meet her obligation of mitigation should not be con-
         strued as a voluntary withdrawal from her former profes-
         sion.  Otherwise, a plaintiff would be put in the intoler-
         able position of choosing between foregoing a source of 
         earnings during the interim before trial or risking an 
         adverse finding on abandonment of her profession.  Such 
         a rule would also work to the disadvantage of employers 
         because the scope of the mitigation obligation necessarily 
         would be relaxed.  It is conceivable that a plaintiff, 
         wronged by discrimination, would decline to take a job 
         that would substantially mitigate damages because such 
         employment could be construed as an abandonment of 
         her former vocation.
    
    Ellis v. Ringgold Sch. Dist., 
    832 F.2d 27
    , 30 (3d Cir. 1987).  
    Here, claimants did not even choose work in an unrelated 
    field, as the plaintiff did in Ellis.  Rather, they did just what 
    the unions have asserted they were obligated to do:  when 
    unable to fill their hours with Local 201 work, they sought 
    and successfully obtained non-union work instead.  See supra 
    Part V.B.  To cut off their back pay now would truly be to 
    apply a Catch-22:  claimants would have been ineligible for 
    back pay had they not tried to obtain non-union work, and 
    
    
    would now be ineligible precisely because they succeeded in 
    obtaining it.
    
         It may be that a reasonable claimant would have known he 
    could have done even better by constantly checking with 
    Local 201 for referrals, although there was record evidence 
    that such constant checking (and the tardiness it would have 
    caused at the claimant's current employment) would have put 
    his non-union work in jeopardy.  See J.A. 663, 761-62, 808-
    11.16  It is also possible that having obtained non-union work, 
    those claimants were satisfied and had no intention of ever 
    returning to Local 201, although they contend they "would 
    have preferred to work out of Local 201 as journeymen" and 
    took the non-union work only because they had no choice.  Pl. 
    Br. at 60.  None of these points was discussed by the Special 
    Master, however, and no findings were made on either side.  
    Accordingly, we must remand the truncation of these awards 
    for further consideration and appropriate application of the 
    law relating to mitigation.
    
         2. Sherman Johnson and John Offer.  The Special Mas-
    ter's decision to truncate the awards of Johnson and Offer 
    presents a different question.  The Master found that John-
    son's medical condition (chronic bronchial asthma) caused him 
    to abandon his pursuit of union referrals in 1976.  J.A. 437.  
    Similarly, the Master found that Offer abandoned rodwork 
    altogether after 1976 because the work was too physically 
    demanding for him.  J.A. 458.  Although both claimants 
    obtained work in other fields, the Master's decision to trun-
    cate their awards did not rest simply on the fact that they 
    took that work, but rather on his finding that the reason they 
    did was because they were no longer able to do the kind of 
    work referred by Local 201.  This does not raise the Catch-
    22 concern noted above, and the Master's finding was not 
    clearly erroneous.  The truncation of these two awards is 
    affirmed.
    
    __________
         16  There was also testimony that returning to the Local after 
    taking a non-union job would have been futile, since rodmen who 
    worked for non-union employers were regarded as "scabs" and not 
    given referrals by the union hiring hall.  See J.A. 903, 1095.
    
    
    
                               VI. Compensatory Damages
    
    
         The unions challenge the Special Master's decision to 
    award compensatory damages to 18 claimants.  They correct-
    ly note that compensatory damages serve only to compensate 
    injuries that result from violations of constitutional or statuto-
    ry rights, and may not be "presumed to flow from every 
    deprivation" of those rights.  Carey v. Piphus, 
    435 U.S. 247
    , 
    263 (1978).  "Where no injury [is] present, no 'compensatory' 
    damages [may] be awarded."  Memphis Community Sch. 
    Dist. v. Stachura, 
    477 U.S. 299
    , 308 (1986).
    
         The Supreme Court, however, has distinguished the imper-
    missible award of compensatory damages--where they are 
    presumed merely from the violation of a right--from the 
    "form of presumed damages [that] may possibly be appropri-
    ate ... [to] roughly approximate the harm that the plaintiffs 
    suffered...."  Id. at 311.  Similarly, in Hobson v. Wilson, 
    this court stated that "in appropriate circumstances the inflic-
    tion of emotional distress may be inferred from the circum-
    stances of the violation."  
    737 F.2d 1
    , 62 n.173 (D.C. Cir. 
    1984).  The critical distinction made by both Memphis and 
    Hobson is that courts may properly infer emotional distress 
    from factual circumstances--and award damages to compen-
    sate for that distress--but may not presume damages from a 
    bare violation of a statutory or constitutional right.  See 477 
    U.S. at 311;  737 F.2d at 62 n.173.
    
         The awards in the instant case are supported by the proper 
    kind of inference.  There can be little doubt that claimants, 
    who were experienced rodmen, suffered emotional distress by 
    having to subject themselves to an unnecessary training 
    program for up to two years before being permitted to take 
    the union entrance exam.  Those circumstances more than 
    adequately support the extremely modest awards granted 
    here, which range from $2,500 to $25,000.
    
         The unions also complain that the Special Master granted 
    compensatory damages to three claimants who did not seek 
    them.  The district court upheld those awards on the basis of 
    Fed. R. Civ. P. 54(c), which provides that "every final judg-
    ment shall grant the relief to which the party in whose favor 
    
    
    it is rendered is entitled, even if the party has not demanded 
    such relief in the party's pleadings."  J.A. 537 (Mem. Op.) 
    (quoting Fed. R. Civ. P. 54(c)).  Although the cited rule may 
    provide the discretionary authority necessary to make the 
    awards to the three claimants, no explanation was offered as 
    to why the Special Master simultaneously failed to award 
    compensatory damages to another claimant for no reason 
    other than that he did "not seek compensatory damages."  
    J.A. 435 n.101 (Sherman Johnson);  see also J.A. 451 (estate of 
    James McGee).  Without such an explanation, we are unable 
    to determine whether this inconsistency reflects a rational 
    distinction or an abuse of discretion, and we therefore remand 
    the compensatory damage awards to James Brown, Paul 
    Brown and Silburn Francis for reconsideration and explana-
    tion.  With those exceptions, the compensatory damages 
    awards are affirmed.
    
                                VII. Punitive Damages
    
    
         The class alleges that the Special Master applied an incor-
    rect standard in denying them an award of punitive damages.  
    The Master stated that "punitive damages will be recoverable 
    for conduct exhibiting malice, evil motive, recklessness or 
    callous indifference to a federally protected right."  J.A. 319 
    (citing Smith v. Wade, 
    461 U.S. 30
    , 52 (1983)).  This is the 
    same standard relied upon by both the majority and the 
    dissent in this circuit's leading case on the issue.  See Kolstad 
    v. American Dental Ass'n, 
    139 F.3d 958
    , 964-65 (D.C. Cir. 
    1998) (en banc), cert. granted, 
    119 S. Ct. 401
     (1998);  id. at 971 
    (Tatel, J., dissenting).17  Moreover, as we also noted in Kol-
    
    __________
         17  In this case, the class' punitive damages claim is based on 42 
    U.S.C. s 1981, since Title VII's punitive damages remedy was not 
    added to the statute until 1991, long after this lawsuit was filed.  It 
    is nonetheless appropriate to apply the principles outlined in Kol-
    stad, which was brought under Title VII, and Smith, which was 
    brought under 42 U.S.C. s 1983, because we have consistently 
    applied the same punitive damages standard under all three stat-
    utes.  See Kolstad, 139 F.3d at 962-65 (applying Smith and s 1981 
    standards in Title VII action);  Barbour v. Merrill, 
    48 F.3d 1270
    , 
    1277 (D.C. Cir. 1995) (applying Smith standard in s 1981 action).
    
    
    
    stad, "punitive damages 'are never awarded as of right, no 
    matter how egregious the defendant's conduct.' "  139 F.3d at 
    965 (quoting Smith, 461 U.S. at 52).  Rather, they are 
    "awarded or rejected in a particular case at the discretion of 
    the fact finder."  Id. (internal quotation omitted);  accord id. 
    at 280 (Tatel, J., dissenting).  We have no basis for overturn-
    ing the Master's discretionary decision here.
    
                              VIII. Prejudgment Interest
    
    
         Finally, both the unions and the class challenge the award 
    of prejudgment interest at a rate of 6%, compounded annual-
    ly, for the entire period of the litigation.  The unions argue 
    that no interest should have been awarded at all or, in the 
    alternative, that no interest should have been awarded for 
    certain periods of time.  The class argues that 6% is too low a 
    rate, and that interest should have been awarded at a variable 
    rate.  We reject all of these contentions and affirm the 
    decision of the district court.
    
         The back pay provision of Title VII "is a manifestation of 
    Congress' intent to make persons whole for injuries suffered 
    through past discrimination," and "[p]rejudgment interest, of 
    course, is an element of complete compensation."  Loeffler v. 
    Frank, 
    486 U.S. 549
    , 558 (1988) (internal citations and quota-
    tions omitted).  For that reason, we have held that "prejudg-
    ment interest 'must be an ordinary part of any award of back 
    pay ... under s 1981.' "  Barbour v. Merrill, 
    48 F.3d 1270
    , 
    1278 (1995) (quoting Williamson v. Handy Button Mach. Co., 
    
    817 F.2d 1290
    , 1297 (7th Cir. 1987)).  The decision as to how 
    to compute prejudgment interest is within the discretion of 
    the district court.  Forman v. Korean Air Lines Co., 
    84 F.3d 446
    , 450 (D.C. Cir. 1996).
    
         In the instant case, both sides cited a variety of circum-
    stances that might support an exclusion of certain time 
    periods on the one hand, or a variable rate of interest on the 
    other.  The district court, after reviewing these arguments, 
    chose the 6% rate for the entire period, principally on the 
    ground that the parties had once consented to that rate.  J.A. 
    521-22.  The unions are wrong in arguing that delays for 
    
    
    
    which they are not responsible mandate tolling of prejudg-
    ment interest.  See Bufco Corp. v. NLRB, 
    147 F.3d 964
    , 967 
    (D.C. Cir. 1998) (refusing to toll interest when NLRB may 
    have been responsible for delay).  The class, on the other 
    hand, is equally wrong in contending that it was an abuse of 
    discretion for the district court to impose a fixed rate in large 
    part because of their earlier concession that such an interest 
    rate would make them whole.  See TI Fed. Credit Union v. 
    DelBonis, 
    72 F.3d 921
    , 928 (1st Cir. 1995) (distinguishing 
    between binding effects of factual and legal stipulations).  We 
    thus affirm the decision of the district court awarding pre-
    judgment interest at the rate of 6%, compounded annually, 
    for the entire period of the litigation.
    
    
         Silberman, Circuit Judge, concurring:  We have strained 
    hard--perhaps too hard--to decide as much of this case as we 
    could.  As our background section indicates, the district 
    court's interminable delays are inexcusable and have caused a 
    great hardship to the parties, particularly the class.  I am 
    terribly concerned that our remand to this district judge is 
    equivalent to dropping the case into a well, and, therefore, we 
    should be prepared to grant extraordinary relief if there is 
    further unjustified delay.
    
         It seems to me that all the district judges--the whole 
    district court--should assume responsibility for unwarranted 
    delays in the processing of cases.  The court of appeals has a 
    rule, the September Rule, which has been vigorously en-
    forced, that prevents any judge from sitting on cases in the 
    fall if he or she has more than three assigned majority 
    opinions outstanding over six months.  I see no reason why 
    the district court could not adopt an analogous rule, more 
    tailored to its circumstances, that would force district judges 
    to process cases in a timely fashion or else be disqualified.  
    The court of appeals can only act episodically as cases are 
    brought to us;  it is not our responsibility to supervise district 
    judges.
    
    
    
         Sentelle, Circuit Judge, concurring and dissenting in 
    part:  I concur in the court's opinion with the exception of 
    Part III.B.7, discussing the eligibility of claimants Paul 
    Brown, James Hicks, and James Brown.  There the court 
    determines that failing the Open Period examination, or 
    failing to take it when offered, does not exclude a claimant 
    from class membership.  The conclusions reached in the 
    court's opinion do not follow from our holding in Berger I. 
    Accordingly, I respectfully dissent.
    
         The language quoted by the court as defining the class is 
    correct, so far as it goes, but it is based on an incomplete 
    examination of our opinion.  As the majority notes, "[t]he 
    union is liable, we said 'to those class members who were 
    experienced workers, but were delayed entry to union ranks 
    by the particular educational prerequisites affecting them 
    from the end of the Open Period until the filing of suit on 
    October 21, 1975.' "  An applicant who failed the Open Period 
    exam, as Paul Brown and James Hicks did, or failed to take it 
    despite being offered an opportunity to do so, as James 
    Brown did, was kept out of the union on the basis of that 
    failure, not on the basis of an impermissible educational 
    prerequisite.
    
         In Berger I, we recognized that the rod trade has histori-
    cally been apprenticeable, and noted that "it stands to reason 
    that on-the-job experience alone may not necessarily teach all 
    that a fully qualified rodman should know."  Berger, 
    843 F.2d 1395
    , 1420.  We pointed to the existence of the Open Period 
    exam as proof that the union could devise an examination that 
    properly tested experienced rodmen to see if they were 
    qualified even though they had not been through an appren-
    ticeship program.  "In our view, the Open Period establishes 
    that experience can qualify one to be a journeyman rodman, 
    and, not incidentally, that the Union is capable of devising 
    an exam that screens out insufficiently competent applicants 
    for journeyman status."  Id. at 1421 (emphasis in original).
    
         Under our analysis, the Union remains free, among other 
         things, to (1) require significant rodman experience be-
         fore an applicant may be admitted to the journeyman 
         exam, (2) offer (cured of discrimination against experi-
         enced workers) both the Apprenticeship and Training 
    
    
         programs, and (3) devise a more exacting or thorough 
         exam for rodmen who eschew classroom training to 
         assure that skills (e.g., reading blueprints) learned in the 
         classroom have been learned on the job (so long, of 
         course, as any such "stepped-up" exam satisfies the 
         bedrock requirements of job-relatedness).
    
    Id.  If we are pointing to the Open Period exam as proof that 
    the union could create an acceptable exam, it does not follow 
    that failure of that exam should not properly be deemed to 
    preclude someone from membership as unqualified.  There-
    fore the proper course for the union to take with regard to 
    someone who failed the Open Period examination was to do 
    precisely what it did, require them to take courses in an 
    apprenticeship program, and then administer the second test. 
    In Berger I, we recognized that it may have been harder, but 
    accepted the increased difficulty.  However, one significant 
    factor, overlooked by the majority opinion, that may explain 
    the difference in passage rates between the two exams is that 
    the rodmen taking the second examination had just finished 
    taking a course designed specifically to help them pass that 
    examination.  Rodmen who could not pass the membership 
    examination and were thus deemed "insufficiently competent 
    applicants for journeyman status" cannot show that they were 
    impermissibly discriminated against by the unions, and are 
    not properly members of the class.
    
    
    
         Garland, Circuit Judge, concurring and dissenting in 
    part:  I concur in the court's opinion with the exception of 
    Part II.  In that Part, the court remands the Special Master's 
    benchmark determination--that is, his calculation of the 
    hours claimants would have worked in the absence of discrim-
    ination.  The questions my colleagues raise about the Mas-
    ter's calculation are not unreasonable ones.  But that is not 
    the test on appeal.  It does not matter that we might have 
    made a different calculation had we been sitting as the triers 
    of fact.  See Anderson v. Bessemer City, 
    470 U.S. 564
    , 573-74 
    (1985).  Instead, to justify remand, appellants must demon-
    strate that the Master's calculation was clearly erroneous.  
    See id.;  9A Wright & Miller, Federal Practice and Proce-
    dure s 2585, at 565 (2d ed. 1995).  Because they have not 
    done so, I would affirm the Master's determination rather 
    than needlessly prolong this decades-old case.
    
                                          I.
    
    
         In order to determine the number of hours the claimants 
    would have worked had they not been subject to discrimina-
    tion, the Special Master consulted Local 201 pension records 
    to calculate the average number of hours a representative 
    group of union workers actually worked during the relevant 
    period.  The court's first objection to the Master's methodolo-
    gy is that he excluded from that group "those who for several 
    years ... worked no hours at all."  J.A. 342-43.  By not 
    including these "zero-hour" workers in calculating the hours 
    of an average worker, the court contends that "the Special 
    Master remove[d] from the equation the risk of disabling 
    injury, or of finding another more desirable job, or whatever 
    other reason a person might not work full time."  Op. at 14.
    
         The inclusion of zero-hour workers may be a reasonable 
    way to account for the risk that an individual claimant would 
    have stopped working even if he had been admitted to the 
    union.  But it is not the only, or even the most direct, way.  
    The most direct way is simply to deny back pay to those 
    claimants who actually did stop working, rather than build 
    into the benchmark the statistical probability that a hypothet-
    ical claimant would have done so.  Not unreasonably, the 
    Special Master chose the direct approach.
    
    
         The Master's benchmark accounted for the risks of injury 
    and attrition as follows.  First, he included within the repre-
    sentative pool those workers whose hours had been reduced 
    by short-term injuries or other absences.  As the court notes 
    in Part IV, the "Special Master's proxy does ... factor in the 
    'average number of days lost due to injury, sickness and 
    attrition.' "  Op. at 34 (quoting J.A. 341).  Second, the Master 
    excluded those who had worked zero hours "for several 
    years," because they were not representative of union mem-
    bers who were actually working during the relevant period.  
    J.A. 342-43.1  Finally, to ensure that a claimant who worked 
    zero hours did not receive a windfall, the Master reduced the 
    pay of claimants where there was "an 'extensive period of 
    unemployment due to injury [that] falls outside [the] statisti-
    cal model of reasonable hours' developed in the benchmark 
    proxy."  Op at 34 (quoting J.A. 445).
    
         I do not disagree that the Master appears to have per-
    formed this last calculus inconsistently.  For that reason, I 
    join Part IV.6 of the court's opinion, which remands certain 
    challenged back pay determinations for an "inquiry into 
    whether each challenged award involves a claimant whose 
    injury-time exceeds th[e] average."  Op. at 35.  But that 
    limited remand is sufficient to remedy the error.  As long as 
    the Master denies claimants back pay for actual absenteeism 
    "so extreme as to be beyond the proxy's statistical average," 
    Op. at 34, there is no reason to require him also to build the 
    probability of lengthy absences into the benchmark.  As the 
    court itself notes in Part II, "[b]oth ... are means of dis-
    counting back pay awards to reflect unavailability for work 
    
    __________
         1  It is important to note that the Special Master did not exclude 
    all zero-hour workers from the proxy group--he excluded only 
    those who had worked zero hours "for several years."  J.A. 342-43.  
    Similarly, defendants' own expert excluded some, but not all, zero-
    hour workers from his preferred benchmark proxy--he excluded 
    "zero-hour rodmen who had died, retired, were incarcerated or 
    permanently disabled."  Op. at 14 (citing J.A. 1381).  Neither the 
    court nor defendants explain why the exclusions made by defen-
    dants' expert were permissible, while those made by the Master 
    were clearly erroneous.
    
    
    
    during the liability period."  Op. at 15.  Even if the 
    probability-based, zero-hour approach were preferable, it can-
    not be clearly erroneous for the Master to have chosen the 
    direct-reduction approach instead.  See Anderson, 470 U.S. at 
    574 ("Where there are two permissible views of the evidence, 
    the factfinder's choice between them cannot be clearly errone-
    ous.").
    
                                         II.
    
    
         The court's second criticism of the Special Master's calcula-
    tion is its asserted failure to recognize that the number of 
    work-hours available for union members during the relevant 
    period was a "fixed pie."  If the claimants had been admitted 
    into the union, the court contends, that fixed pie of hours 
    would have been divided among a greater number of workers.  
    Hence, each union member would have worked fewer hours 
    than union members actually worked during the period.  
    There are two reasons to reject this critique.
    
         First, defendants did not make this argument in their 
    briefs before this court.  Indeed, the term "fixed pie" cannot 
    be found anywhere therein.  See Def. Br. at 24-32;  Def. 
    Reply Br. at 4-6.  We routinely and for good reason refuse to 
    consider contentions not raised in a party's briefs.  See Boggs 
    v. Rubin, 
    161 F.3d 37
    , 42 (D.C. Cir. 1998) (holding that "[w]e 
    will not consider at this late stage an argument that the 
    appellant failed to raise" in his briefs);  Diamond Walnut 
    Growers, Inc., v. NLRB, 
    113 F.3d 1259
    , 1263 (D.C. Cir. 1997) 
    (en banc) ("[I]t is well-established ... that we do not consider 
    arguments not presented to us.").  Although it is not impossi-
    ble to tease the recipe for a fixed-pie argument out of a single 
    sentence in which defendants described the calculations per-
    formed by their own expert, their briefs did not argue that a 
    fixed-pie problem rendered the Special Master's calculations 
    clearly erroneous.  As we have said in another context, a 
    reviewing body "need not sift pleadings and documents to 
    identify arguments that are not stated with clarity by a 
    petitioner."  Bartholdi v. FCC, 
    114 F.3d 274
    , 279 (D.C. Cir. 
    1997) (internal quotations omitted);  see also United States v. 
    
    
    
    Gilliam, No. 97-3084, slip op. at 20 n.10 (D.C. Cir. Feb. 26, 
    1999) ("[T]he court will not construe the briefs to raise an 
    argument that is hinted at but never stated.").2
    
         Second, there is substantial support in the record for the 
    Master's conclusion that "there really [was] no fixed pie" of 
    available hours.  J.A. 339.  As the court explains, the Local 
    referred work to both union members and non-union workers.  
    The defendants' expert assumed that had claimants become 
    members of the union, they would have displaced non-union 
    workers first.  There would thus be no fixed-pie problem, the 
    expert said, as long as the hours referred to non-union 
    workers in a given year were more than the potential "claim-
    ant hours"--which he defined as the product of the number of 
    eligible claimants and the mean hours worked by union 
    members that year.  J.A. 1383 (report of defendant's expert).
    
         Examination of two charts prominently displayed in defen-
    dants' own brief reveals that in fact, the number of hours the 
    Local referred to non-union workers did exceed the number 
    of potential claimant hours every year through 1981.  Def. Br. 
    at 15, 28.  That is because in each of those years the union 
    referred in excess of 100,000 hours to non-union workers, 
    more than enough to accommodate 173 claimants without 
    displacing any union members.3  Hence, even assuming that 
    
    __________
         2  To a lesser extent, the zero-hour argument discussed above 
    suffers from the same disability.  Although one of defendants' 
    briefs did use the term "zero-hour" (once), it did so only in 
    describing the work of defendants' expert.  It did not expressly 
    argue that the failure to include zero-hour workers rendered the 
    Master's benchmark clearly erroneous.
    
         3  The chart on page 15 of defendants' brief discloses the 
    number of hours the union referred to non-union workers in each 
    year.  The chart on page 28 shows the mean union-member hours 
    for each year as determined by defendants' expert.  When the 
    latter figures are multiplied by the 173 putative class members, the 
    resulting claimant hours are less than the non-union hours for every 
    year through 1981.
    
    
    the union could not have attracted additional work for addi-
    tional members, there simply was no fixed-pie problem 
    through 1981.4  If there were an error in the Master's 
    calculation, then, it would apply only to awards for years after 
    1981--and only one claimant received such an award.  At 
    most, the fixed-pie theory would necessitate a remand of the 
    award to Eldridge Harmon, who received $2,075 for 1985-86.
    
         But the court is also factually incorrect in stating that 
    "[t]here is no evidence in the record to suggest that there was 
    additional work in the D.C. area for Local 201 rodmen" 
    beyond that actually handled by its union members and non-
    union referrals.  Op. at 16.  Defendants' own briefs provide 
    the contrary evidence, demonstrating that during the entire 
    relevant period, Local 201 had more job requests from em-
    ployers than both its union and non-union workers could 
    absorb.  Defendants state that from 1972 to 1975, "Local 201 
    was unable to fill 4,432 jobs due to an insufficient number of 
    workers seeking jobs through the hiring hall."  Def. Br. at 14 
    (citing J.A. 274-75).  And from 1976 to 1986, "Local 201 was 
    unable to fill 1,649 jobs."  Id. at 15;  see also id. at 60 ("Even 
    after the 1972-75 'full employment' period, Local 201-referral 
    jobs went unfilled for lack of applicants.").  Defendants' 
    evidence makes clear that this circumstance existed in every 
    year for which there are records, see J.A. 275, despite the fact 
    that the "union never deliberately let a job go unfilled."  Def. 
    Br. at 14.  Hence, the defendants' own briefs provide the 
    "prima facie showing that additional hours were available to 
    Local 201" upon which the court insists.  Op. at 16.5
    
    __________
         4  This roughly accords with the concession of defendants' own 
    expert that in the 1970s there would have been sufficient hours 
    available for the claimants had they been admitted to the union.  
    See J.A. 339 (citing expert's testimony).
    
         5  The court states that the fact that jobs went unfilled does not 
    necessarily mean that the union had enough work for the claimants, 
    since it might be explained merely by "[f]luctuations on a given day 
    that would result in a specific job referral being listed as unfilled."  
    Op. at 18.  But this theoretical possibility, like the year-to-year 
    disparities to which the court also points, is hardly sufficient to 
    justify a conclusion that the Master's determination was clearly 
    
    
    
         Finally, the fact that the union had to turn down jobs also 
    undermines the court's declaration that "[c]ommon sense and 
    experience suggest that a union will attempt to bring as many 
    projects as possible under union control."  Op. at 16.  That 
    may be the case where a union and its non-union referrals are 
    able to handle all the work they can bring in.  But where a 
    local is already turning down unsolicited job referrals, it has 
    no incentive to bring still more projects under its control.  
    Under these circumstances, neither common sense nor expe-
    rience militates against the Master's finding that there was 
    no fixed pie.  J.A. 339.6
    
                                         III.
    
    
         The burden is on the appellants to establish that the 
    decision below was clearly erroneous.  See Bellevue Gardens, 
    Inc. v. Hill, 
    297 F.2d 185
    , 187 (D.C. Cir. 1961);  9A Wright & 
    Miller s 2585, at 565.  Because they have not met that 
    burden, there is no reason for us to prolong the final resolu-
    tion of plaintiffs' back pay awards by remanding the Special 
    Master's benchmark determination for further consideration.
    
    __________
    erroneous.  See Anderson, 470 U.S. at 573-74.  The court also 
    contends that defendants "made a prima facie showing that the 
    hours were not available" for the claimants, based on evidence of 
    "the declining hours referred out of the hall and [on] evidence 
    [defendants] introduced of the declining market share available to 
    the union."  Op. at 16.  But it is the gross hours potentially 
    available for the claimants, not the evidence of trends and percent-
    ages, that is relevant to the validity of the fixed-pie theory.
    
         6  For the same reasons, and contrary to the court's contention, 
    the Special Master did not shift the burden of proof to defendants 
    by characterizing the fixed-pie theory as "at best speculative."  J.A. 
    340.  Indeed, the defendants' expert himself described the theory in 
    words of speculation.  See J.A. 1383 (stating that the benchmark 
    "may require [an] adjustment ... [to] reflect[ ] the fixed number of 
    union-referred hours") (emphasis added);  id. at 1384 (stating that a 
    fixed-pie adjustment would be required "if there are no permitmen 
    and travelers working in a given year") (emphasis added).