Jessie Berger v. Iron Workers Reinforced Rodmen Local 201, International Association of Bridge, Structural and Ornamental Iron Workers

Opinion for the Court filed by EDWARDS, STARR and D.H. GINSBURG, Circuit Judges. PER CURIAM: This case involves a class action brought by eight black construction workers alleging racial discrimination under 42 U.S.C. § 1981 (1982) and Title VII of the Civil Rights Act of 1964, 42 U.S.C. § 2000e et seq. (1982). The plaintiffs charged that various requirements for admission to Local 201 of the Iron Workers Reinforced Rodmen (the “Union”) and to its international union, the International Association of Bridge, Structural and Ornamental Iron Workers (the “International”), discrimina-torily denied black rodmen the benefits of union membership. The plaintiffs sued both the Union and the International, along with the Union’s Apprenticeship Committee, the National Iron Workers and Employers Training Program, and the Construction Contractors Council/AGC Labor Division, Inc. (“CCC”), an organization that negotiated collective bargaining agreements with the Union on behalf of most employers of rodmen in and around Washington, D.C. Suit was filed in 1975, the case went to trial in 1981, and the District Court rendered its decision in 1985. The trial court’s decision raises very difficult problems for this court. Having received over eighty-five pages of proposed findings of fact and conclusions of law from the plaintiffs in December 1981, the District Court adopted them almost verbatim after a lapse of three and a half years, retaining most of the plaintiffs’ typographical errors but deleting their references to the record, thus hampering review. Not surprisingly, the District Court found all of the defendants liable for all of the alleged violations of Title VII and section 1981. The court’s subsequent remedial order again copied the plaintiffs’ proposal; an amended order was issued in April 1986. The defendants then appealed from the trial court’s decision and order. In considering this appeal, we embrace the view expressed by a number of circuits in strongly disapproving the procedure followed by the trial court in reaching judgment in this case. See, e.g., EEOC v. Federal Reserve Bank, 698 F.2d 633, 639-42 (4th Cir.1983), rev’d on other grounds sub nom. Cooper v. Federal Reserve Bank, 467 U.S. 867, 104 S.Ct. 2794, 81 L.Ed.2d 718 (1984), and cases cited therein. While “the fact that the trial judge has adopted proposed findings does not, by itself, warrant reversal,” “it does raise the possibility that there was insufficient independent evaluation of the evidence and may cause the losing party to believe that his position has not been given the consideration it deserves.” Photo Elecs. Corp. v. England, 581 F.2d 772, 777 (9th Cir.1978). Indeed, this is surely the case here, where the appellants assert that “the District Court’s uncritical acceptance of plaintiffs’ proposed findings ... did not provide the even-handed consideration of the evidence necessary to a fair adjudication of the issues.” Brief of Appellant CCC at 28. After ten years of litigation in District Court, the appellants had a right to expect something more. Because of the state of the record on appeal, this case was needlessly given “complex” treatment under this circuit’s Case Management Plan, and then it required more exacting scrutiny than this court ordinarily accords the District Court’s findings. A meticulous review of the District Court’s conclusions uncovered a number of clearly erroneous factual findings and several errors of law. We therefore reverse in part and affirm in part. *1405 I. Background Rodmen are construction workers who handle and position steel rods for reinforcing concrete and other building materials. Most of the rodmen who worked in the Washington, D.C., area in the early 1970s were employed through referrals by the Union, pursuant to a series of collective bargaining agreements between the Union and CCC. The Union’s referral system ensured that Union members were offered employment opportunities before jobs were made available to non-Union permit workers who applied for positions through the Union’s hiring hall. When Washington’s commercial construction industry entered a slump in 1975, Union membership became especially valuable, because limited employment prospects prevented permit workers from obtaining regular employment. Admission to the Union always has been by examination. The prerequisites for taking the entrance exam, however, have varied over time. Four different sets of prerequisites are relevant to the adjudication of this case. 1965-February 1971. During this period, there were two routes to the exam: (1) by permission of the Union’s Executive Committee, which could grant leave, in its discretion, to rodmen with an unspecified amount of experience to take the exam; and (2) by completion of the two-year Apprenticeship Program, admission to which was contingent upon the applicant (a) being between 18 and 31 years of age, (b) possessing a high school diploma, and (c) being physically fit. February 1971-June 1971. There were also two paths to the exam at this time. (1) Those who completed the Apprenticeship Program could take the usual exam. (2) All rodmen with two years’ experience were eligible to take a special exam — not the one given by the Union before or after this period — which had a higher failure rate. Because all experienced rodmen were allowed to sit an entrance exam without participating in a Union-supervised educational program, these five months are referred to as the “Open Period.” June 1971-September 1972. Throughout this period, only rodmen who had completed the Apprenticeship Program were permitted to take the exam. September 1972-October 1975. Once again, there were two tracks to the exam. (1) Completion of the Apprenticeship Program, whose admission requirements were unchanged, provided a ticket to the exam. (2) In addition, the Training Program was established, primarily to allow experienced minority workers to gain access to the exam and thus to Union membership. Although race was not a criterion for admission, special efforts were made to recruit minority workers. Participants in the Training Program had to be (a) physically fit, and (b) 31 years of age or older. Unlike the Apprenticeship Program at that time, the Training Program lacked a high school diploma requirement. 1 Moreover, trainees —but not apprentices — were sometimes allowed to take the exam after a minimum of six months’ instruction, even though both educational programs were two years long. Throughout this entire period, no applicant was guaranteed acceptance into an educational program merely because he met the entrance requirements. Enrollment was always limited, and many who qualified for admission were either rejected or not permitted to apply. Once admitted to either program, however, no enrollee was asked or compelled to discontinue participation because of unsatisfactory performance; the only ground for expulsion was failure to meet one of the enrollment requirements described above. Completion of one of the programs resulted almost automatically in Union membership, since virtually all examinees, with the exception of those tested during the Open Period, passed the test. 2 *1406 Prior to the passage of Title VII, the membership of Local 201 was overwhelmingly white. The Union’s racial composition changed after 1965, when Title VII took effect, but only gradually. At the start of 1967, only four of approximately 200 members were black. Trial Finding (“Tr.F.”) 63. Four years later, the Union numbered 16 black and 260 white members. Tr.F. 63. Although black membership increased markedly with the advent of the Open Period, the percentage of blacks entering the Union was plainly smaller than the percentage of blacks among non-Union permit workers. For example, while approximately 40% of those admitted to the Union in the three years prior to the initiation of this suit were black, Brief of Local 201 at 18, blacks comprised 50-60% of nonUnion workers seeking employment through the Union’s hiring hall. Brief of Appellees at 7. On October 21, 1975, six black rodmen who were not members of the Union filed suit against all of the defendants, alleging racial discrimination in violation of Title VII and section 1981. The gravamen of the plaintiffs’ complaint is that the preconditions to Union membership in the early 1970s — in particular, the requirement that apprentices hold a high school diploma and the requirement that rodmen enroll in either the Apprenticeship or the Training Program before taking the Union’s entrance exam — excluded a higher proportion of blacks than whites from Union membership and that these preconditions could not be justified on work-related grounds. Pursuant to a pretrial stipulation by the parties, the District Court certified the following two classes on July 26, 1976: 1) All black persons who have applied for or sought, from representatives of Local 201 or the International, membership in Local 201 and, in connection therewith, the International or who have applied for or sought, from representatives of Local 201, the Apprenticeship Program or the Training Program, admission to the Apprenticeship Program and/or the Training Program and who have been or might be excluded from Local 201 and, in connection therewith, the International or the Apprenticeship Program or the Training Program or any of the above by the alleged discriminatory practices of the Defendants and who could have filed timely charges with the EEOC when their class representatives filed such charges or who could have filed timely lawsuits when the class representatives filed the instant lawsuit. 2) All black persons who have been referred for employment by Local 201 or who have applied to Local 201 for referral for employment by any means, including filling out a referral slip, or presenting themselves at Local 201 and requesting representatives of Local 201 to refer them for work, and who have been or might be discouraged from applying for membership in Local 201 and in connection therewith, the International, and/or Apprenticeship Program and/or the Training Program by the allegedly racially discriminatory practices of the Defendants and who could have filed timely charges with the EEOC when their class representatives filed such charges or who could have filed timely lawsuits when their class representatives filed the instant lawsuit. Order (July 26, 1976), reprinted in Record Excerpts (“R.E.”). On March 6, 1978, the District Court allowed the six named plaintiffs to amend their complaint by adding two black rod-men — Simmons and McMillian — because it appeared that the original six might not include suitable representatives of both classes. Memorandum and Order (Mar. 6, 1978), reprinted in R.E. After the District Court denied separate motions for summary judgment by the Apprenticeship Committee, the International, and CCC, the case was tried during the summer and fall of 1981. More than three *1407 and a half years later, on June 7, 1985, the District Court issued its Trial Findings, merely copying, with insignificant changes, the proposed findings of fact and conclusions of law submitted by the plaintiffs on December 18, 1981. The court found all of the defendants liable for the allegedly racially discriminatory admissions policies of the Union dating back to at least 1965, as well as for retaliatory actions alleged to have been taken against several named plaintiffs. The District Court issued a remedial order on December 10, 1985, which was superseded by an Amended Order handed down on April 10, 1986. The Amended Order increased access to the entrance exam or to Union membership for experienced black rodmen, and provided for future proceedings to determine awards of backpay and damages. In addition, the court ordered the Union to return money collected from class members pursuant to a uniform levy on all Union workers to pay the Union’s legal expenses in connection with this action. The defendants appeal from the District Court’s Trial Findings and Amended Order, contending that many of the District Court’s findings of fact were clearly erroneous, that a large number of its legal conclusions were also mistaken, and that the court abused its discretion in choosing remedies. II. Standard of Review Federal Rule of Civil Procedure 52(a) provides in part that “[findings of fact... shall not be set aside unless clearly erroneous, and due regard shall be given to the opportunity of the trial court to judge the credibility of the witnesses.” The appellants have asked this court, however, to perform a more rigorous appraisal of the District Court’s findings than this rule prescribes. They contend that the trial judge’s almost verbatim transcriptions of the plaintiffs’ extensive proposals do not constitute genuine “findings” of fact, and thus that de novo review, or something approaching it, is appropriate in the unique circumstances of this case. We disagree. Although we strongly disapprove of the District Court’s wholesale adoption of the plaintiffs’ proposed findings — especially in a case of this magnitude—we adhere to the view that de novo review “would be wholly inconsistent with the function of an appellate court.” Southern Pac. Communications Co. v. AT & T, 740 F.2d 980, 984 (D.C.Cir.1984), cert. denied, 470 U.S. 1005, 105 S.Ct. 1359, 84 L.Ed.2d 380 (1985). An appellate court is generally ill-equipped to conduct de novo review, and the assignment of that task to courts of appeals would waste judicial resources. De novo review, moreover, would be contrary to the plain meaning of Rule 52(a), which requires courts to set aside factual findings only if they are “clearly erroneous.” It would also contravene the settled doctrine of this court and the Supreme Court. As the Court recently stated: We, too, have criticized courts for their verbatim adoption of findings of fact prepared by prevailing parties, particularly when those findings have taken the form of conclusory statements unsupported by citation to the record.... Nonetheless, our previous discussions of the subject suggest that even when the trial judge adopts proposed findings verbatim, the findings are those of the court and may be reversed only if clearly erroneous. Anderson v. City of Bessemer City, 470 U.S. 564, 572, 105 S.Ct. 1504, 1510, 84 L.Ed.2d 518 (1985). 3 *1408 We adhere to the standard of review enunciated in Rule 52(a) and shall set aside factual findings only if we deem them clearly erroneous; however, we note that the function of appellate review that we must undertake in a case of this sort is substantially different (and more difficult) than what is normally required. In Southern Pacific, we explained that when a trial judge “abdicate^] to a party his duty to provide a reasoned explanation for his decision” and merely copies submitted proposals, it is incumbent on this court to check the adopted findings against the record “with particular, even painstaking, care.” 740 F.2d at 984; see also Sealy, Inc. v. Easy Living, Inc., 743 F.2d 1378, 1385 n. 3 (9th Cir.1984) (“special scrutiny”); EEOC v. Federal Reserve Bank, 698 F.2d 633, 639-42 (4th Cir.1983) (“careful scrutiny” is necessary and findings must be “more narrowly” examined when trial court merely reprints proposed findings), rev’d on other grounds sub nom. Cooper v. Federal Reserve Bank, 467 U.S. 867, 104 S.Ct. 2794, 81 L.Ed.2d 718 (1984); Amstar Corp. v. Domino’s Pizza, Inc., 615 F.2d 252, 258 (5th Cir.), cert. denied, 449 U.S. 899, 101 S.Ct. 268, 66 L.Ed.2d 129 (1980). The “special care” we devote to reviewing “findings [that] were not initially penned by the district judge,” Valentino v. United States Postal Serv., 674 F.2d 56, 60 n. 2 (D.C.Cir.1982), differs from that which we ordinarily display, not in the test that we apply to a particular finding of fact — individual findings will only be reversed if clearly erroneous — but in the volume of evidence we sift in judging the correctness of such findings and in the number of discrete findings we review without benefit of express, thoroughly supported allegations of error by the opposing party. Although we undertake with great reluctance what in this case has proven a Herculean task, the District Court’s inexplicable failure to reason independently and to address the defendants’ leading arguments leave us no choice. III. Class Action Issues The appellants raise four objections to the District Court’s certification of the two plaintiff classes in this case. First, they argue that the District Court failed to ascertain whether the requirements of Federal Rule of Civil Procedure 23(a) were met with respect to each of them, and that this court should therefore remand for such a determination. Second, the appellants contend that the District Court failed to set temporal boundaries to the classes, and that a remand is necessary to allow it to do so. Third, the appellants submit that none of the named plaintiffs adequately represents the class of those black permit workers who were allegedly injured by the Apprenticeship Program’s high school diploma requirement in violation of Title VII and section 1981. Fourth, they claim that the plaintiff class should be limited to those who actually applied for admission to the Union or one of its educational programs, and that the second class of “discouraged” nonapplicants should be decertified. We find the first two arguments merit-less. We agree, however, that none of the named plaintiffs is a suitable representative of those who were allegedly wronged by the Apprenticeship Program’s high school diploma requirement; accordingly, that portion of the plaintiffs’ case should not have been permitted to go forward to judgment, and the District Court’s decision on this issue must be reversed. The appellants’ fourth objection is misguided insofar as it applies to the plaintiffs’ remaining challenge to the Union’s requirement that experienced rodmen enroll in an educational program before taking the entrance exam. *1409 A. Possible Failure to Conduct a Rule 23(a) Analysis The Supreme Court has stated that “a Title VII class action, like any other class action, may only be certified if the trial court is satisfied, after a rigorous analysis, that the prerequisites of Rule 23(a) have been satisfied.” General Tel. Co. v. Falcon, 457 U.S. 147, 161, 102 S.Ct. 2364, 2372, 72 L.Ed.2d 740 (1982). The two classes in this case were conditionally certified upon stipulation by all the parties. Order (July 26,1978), reprinted in R.E. It is unclear, however, whether the District Court performed the required analysis regarding the prerequisites of Rule 23(a). Nevertheless, we find the District Court’s failure to articulate the reasons for its decisions an insufficient reason to remand. The defendants have not pointed to any possible errors in the District Court’s definition of the classes apart from those considered separately below. See Brief of Local 201 at 34-39. Nor have we identified any ourselves. In the absence of any reason to suspect that the District Court’s decisions in this regard were mistaken, we cannot label the court’s silence an abuse of discretion warranting a remand. See Postow v. OBA Fed. Sav. & Loan Ass’n, 627 F.2d 1370, 1380 n. 24 (D.C.Cir.1980). B. Temporal Limits to the Classes The appellants contend that, while the class definitions contained in the 1976 certification order and reproduced in the Amended Order “purport[ ] to accord with relevant time frames,” the District Court’s “numerous errors in construing what such limitations actually mean ... require a remand for the purpose of specifically defining both backward and forward class limitations by date, even if [the] class definition[s] (at least as to time) [are] to be adhered to.” Brief of Local 201 at 49. We reject this contention as frivolous. The appellants, by their own admission, do not find fault with the temporal aspects of the District Court’s class definitions. Hence, there is no reason at all to remand on this point. To the extent that the appellants quarrel with the District Court's application of this unquestionably acceptable definition in specifying remedies, their objections are properly considered under that heading. C.The Ability of Class Representatives to Challenge the Apprenticeship Program’s High School Diploma Requirement As the appellants correctly note, the plaintiffs’ challenge to the Apprenticeship Program’s admission requirements focused exclusively on the rule that apprentices hold high school diplomas, and the District Court found this requirement alone to violate Title VII and section 1981. See Brief of Local 201 at 41; Tr.F. 85-100. No objections were raised to the requirements that apprentices be physically fit or that they be under thirty-one years of age. The Supreme Court has “repeatedly held [that] a class representative must be part of the class and ‘possess the same interest and suffer the same injury’ as the class members.” East Tex. Motor Freight Sys. v. Rodriguez, 431 U.S. 395, 403, 97 S.Ct. 1891, 1896, 52 L.Ed.2d 453 (1977) (quoting Schlesinger v. Reservists Comm. to Stop the War, 418 U.S. 208, 216, 94 S.Ct. 2925, 2930, 41 L.Ed.2d 706 (1974)). The plaintiffs may therefore only bring a class action challenging the high school diploma requirement of the Apprenticeship Program if one of the named plaintiffs was allegedly injured by that requirement. Hence, this part of the action may not proceed unless one of the eight named plaintiffs was, during the Title VII or section 1981 limitations period, refused admission to the Apprenticeship Program or discouraged from applying for admission because he lacked a high school diploma, notwithstanding his having met the age and fitness requirements at that time. Two of the named plaintiffs — McMillian and Simmons — graduated from high school, and thus may not serve as class representatives. Tr.F. 18-19. The other six did not have high school diplomas at times relevant to this suit. All of them, however, either were too old to challenge the high school diploma requirement within the statutory *1410 limitations periods, or were not injured by it because they had no interest in enrolling in the Apprenticeship Program during those periods. A plaintiff may bring a Title VII action only if he has first filed charges with the Equal Employment Opportunity Commission (“EEOC”) within 180 days of suffering injury in violation of the statute. 42 U.S.C. § 2000e-5(e) (1982). Thus, one of the six named plaintiffs without a high school degree could challenge the Apprenticeship Program’s high school diploma requirement only if, within 180 days of filing charges with the EEOC, he was under 31 years of age and physically fit, and if he was at that time denied admission or was discouraged from applying because he lacked a high school diploma. Plaintiff Lewis was the first of the named plaintiffs to file charges with the EEOC. He did so either in December 1974, or on January 13, 1975, depending upon which of the District Court’s inconsistent findings is correct. Compare Tr.F. 5 with Tr.F. 15. The 180-day limitations period under Title VII therefore began to run in June or July 1974. However, Lewis had turned 31 prior to that date, as had all of the other plaintiffs who had not graduated from high school. 4 None of the six could therefore demonstrate that he was injured by the Apprenticeship Program’s high school diploma requirement after June 1974, because all were or would have been excluded by virtue of their age, and the age limit was never challenged or found to be discriminatory. Hence, the class action challenge to the high school diploma requirement may not be brought under Title VII. Although section 1981 does not contain its own statute of limitations, 42 U.S.C. § 1988 requires that the most nearly analogous District of Columbia statute of limitations be applied to suits under section 1981. In Banks v. Chesapeake & Potomac Tel. Co., 802 F.2d 1416 (D.C.Cir.1986), this court held that the most closely analogous period for purposes of section 1981 is that set by D.C. Code Ann. § 12-301(8) (1981), which specifies a three-year limitations period for personal injury claims not specified elsewhere in the D.C. Code. In reaching that decision, however, the court faced only the question whether the three-year statute of limitations for specified personal injury claims or the one-year period provided by the D.C. Human Rights Act, D.C. Code Ann. § 1-2544 (1981), applied to suits under section 1981. The court did not determine whether the one-year limitations period for most intentional torts, D.C. Code Ann. § 12-301(4), or the three-year period applicable to other personal injuries is more appropriately applied to section 1981 suits. Although a majority of the three-judge panel argued at length that the three-year limitations period applied, see Banks, 802 F.2d at 1426-29, the majority recognized that it was “considerpng] the issue in dicta only, and only in order to answer” objections raised in a concurring opinion. Id. at 1427. The question whether a one-year or a three-year limitations period governs actions under section 1981 therefore remains open. We need not resolve it now. Regardless of which limitations period is correct, none of the six original plaintiffs fulfilled the requirements for challenging the high school diploma requirement under section 1981. If the one-year period should be applied, then the plaintiffs’ suit was plainly foreclosed, because all six turned thirty-one prior to October 21, 1974, the date one year before suit was filed. See note 4 supra. If the three-year period is proper, then five of the six would once again have been excluded from the Apprenticeship Program by reason of age; only Lewis was under thirty-one years of age on October 21, 1972. However, Lewis testified at trial that he did not apply for admission to the Apprenticeship Program between October 21, 1972, and his thirty-first birthday, and he never claimed that he would have applied *1411 had there been no high school diploma requirement. He apparently only thought of applying to the Apprenticeship Program after he had turned thirty-one: “I didn’t apply for the apprenticeship program because they said you couldn’t get in over 30.” Transcript (“Tr.”) at 471. Since Lewis did not allege injury by the Apprenticeship Program’s high school diploma requirement, he cannot serve as the representative of a plaintiff class contesting the lawfulness of that requirement under section 1981. The class action challenging the high school diploma requirement under both Title VII and section 1981 therefore fails for want of a suitable representative. 5 The plaintiffs did, however, satisfy the jurisdictional prerequisites for assailing the Union’s requirement that experienced workers enroll in either the Apprenticeship or the Training Program before taking the entrance exam. Although the appellants have not denied that the named plaintiffs adequately represent the class of those allegedly injured by this requirement, and thus have waived any objection they might have raised, see Banks, 802 F.2d at 1427, we note that Kirkland was experienced, physically fit, and desirous of taking the entrance exam within six months of the filing of charges with the EEOC on his behalf and within six months of the filing of this law suit. See Tr.F. 6, 14. Because this requirement was in effect since the end of the Open Period in June 1971, all class members who were injured by the requirement after that date may join in this suit and any recovery under it. D. Should Discouraged Nonapplicants Be Part of the Plaintiff Class? The appellants contend that the class definition should not have included “persons who have never actually applied for membership in Local 201, or for admission to the training or apprenticeship programs.” Brief of Local 201 at 46. This objection apparently derives from a misunderstanding of at least part of the plaintiffs’ theory of liability. The plaintiffs’ contention with respect to the educational prerequisite for taking the entrance exam, if not with regard to the Apprenticeship Program’s high school diploma requirement, is that compelling experienced rod-men to participate in some educational program for six months or more before allowing them to take the exam was itself unlawful. There is no reason why those who were unwilling to subject themselves to an allegedly unlawful regimen, but who would have taken the exam had this obstacle not been placed iii their path, may not challenge that requirement. We therefore see no merit in the appellants’ objection insofar as it applies to the plaintiffs’ attack on the instructional prerequisite to sitting the entrance exam. IV. Plaintiffs’ Statistical Proof of Discrimination A. Legal Framework 1. Law Governing Establishment of a Prima Facie Case by Statistical Proof The legal framework governing plaintiffs’ claims is straightforward. Under now-familiar Title VII law, plaintiffs bear the burden of establishing a prima facie case of racial discrimination. See Texas Dep’t of Community Affairs v. Burdine, 450 U.S. 248, 101 S.Ct. 1089, 67 L.Ed.2d 207 (1981); United States Postal Serv. Bd. of Governors v. Aikens, 460 U.S. 711, 103 S.Ct. 1478, 75 L.Ed.2d 403 (1983). In seeking to prove that facially neutral employment criteria fall more harshly on blacks than whites, plaintiffs may rely on statistical evidence tending to show that those criteria “select applicants for hire or pro *1412 motion in a racial pattern significantly different from that of the pool of applicants.” Albemarle Paper Co. v. Moody, 422 U.S. 405, 425, 95 S.Ct. 2362, 2375, 45 L.Ed.2d 280 (1975); see also Griggs v. Duke Power Co., 401 U.S. 424, 430-31, 91 S.Ct. 849, 853, 28 L.Ed.2d 158 (1971). If the racial makeup of a selected group (in this case, those who became Union members) differs significantly from that of the pool from which it was selected, discrimination may be inferred. See International Bhd. of Teamsters v. United States, 431 U.S. 324, 335 n. 15, 339 n. 20, 97 S.Ct. 1843, 1854 n. 15, 1856 n. 20, 52 L.Ed.2d 396 (1977); Hazelwood School Dist. v. United States, 433 U.S. 299, 307-08, 97 S.Ct. 2736, 2741, 53 L.Ed.2d 768 (1977). Once this is demonstrated, a prima facie case has been established, and the burden shifts to defendants to articulate a legitimate non-discriminatory reason for the challenged employment practice. Burdine, 450 U.S. at 253, 101 S.Ct. at 1093; McDonnell Douglas Corp. v. Green, 411 U.S. 792, 802-03, 93 S.Ct. 1817, 1824, 36 L.Ed.2d 668 (1973); McKenzie v. Sawyer, 684 F.2d 62, 71 (D.C.Cir.1982). Defendants may also attempt to undermine plaintiffs’ prima facie case by attacking the validity of plaintiffs’ statistical evidence, or by introducing statistical evidence of their own showing that the challenged practice did not have racially disproportionate results. See Teamsters, 431 U.S. at 360, 97 S.Ct. at 1867; Segar v. Smith, 738 F.2d 1249, 1268 (D.C.Cir.1984), cert. denied, 471 U.S. 1115, 105 S.Ct. 2357, 86 L.Ed.2d 258 (1985). The degree of disparity between the expected and actual racial composition of the membership necessary to support an inference of discrimination is commonly viewed in terms of standard deviations. The Supreme Court has stated that a difference of approximately two to three standard deviations between expected and actual results is sufficient to demonstrate that the disparity is the product of something other than chance. See Castaneda v. Partida, 430 U.S. 482, 496 n. 17, 97 S.Ct. 1272, 1281 n. 17, 51 L.Ed.2d 498 (1977). There is, however, a large gap between two and three standard deviations, and thus the Supreme Court’s teaching in this respect has not been entirely dispositive. Under this circuit’s precedent, in most instances a difference of just under two standard deviations has been deemed sufficient to establish a prima facie case. See Palmer v. Shultz, 815 F.2d 84, 91-92 (D.C.Cir.1987). As we shall presently see, the statistical disparities in this case are well above two standard deviations; we are thus not faced with nettlesome issues such as whether 1.96 or 2 standard deviations ought to be the standard, or whether a one-tailed or two-tailed statistical test applies. 6 A difference of two standard deviations corresponds roughly to a five percent probability that the disparity is the result of chance; this five percent standard is commonly referred to as the “.05 level of significance.” See Segar v. Smith, 738 F.2d at 1282-83. Thus, if the likelihood that a fluctuation from expected results occurred by chance is five percent or less, a statistically significant difference is proved, and a prima facie case of discrimination is established. It is, of course, elementary that intent to discriminate is a necessary element of Title YII disparate treatment cases. 7 But here too, statistics play an important part. The basic office of statistical proof is to seek to eliminate non-discriminatory explanations for racial disparities; thus a statistically valid showing of a substantial disparity *1413 between expected and actual results may give rise to an inference of discriminatory intent. Teamsters, 431 U.S. at 336 n. 15, 97 S.Ct. at 1854 n. 15; Hazelwood, 433 U.S. at 307-08, 97 S.Ct. at 2741. What is more, this court has squarely held that, even absent specific anecdotal evidence of discrimination, statistical proof alone may establish a prima facie case of intentional discrimination. Segar v. Smith, 738 F.2d at 1277-79, 1286-87; see also McKenzie v. Sawyer, 684 F.2d 62, 71 (D.C.Cir.1982) (“Statistics alone will suffice to show illegally discriminatory treatment, if they are condemning enough.”) In the course of enunciating this rule, the court in Segar rejected the proposition that to establish intentional discrimination a showing of “gross disparities,” rather than mere statistically significant disparties, is required. Segar v. Smith, 738 F.2d at 1277-78. 2. Law Governing Rebuttal of a Statistically Based Prima Facie Case Once plaintiffs establish a prima facie case, the burden shifts to the defendants to articulate a legitimate non-discriminatory explanation for the statistical disparity. See Segar v. Smith, 738 F.2d at 1267-68; Davis v. Califano, 613 F.2d 957, 961-62 (D.C.Cir.1979). 8 Alternatively, defendants can also meet their burden by demonstrating that plaintiffs’ statistics are so flawed as to be meaningless, or by introducing alternative statistical evidence. See Dothard v. Rawlinson, 433 U.S. 321, 331, 97 S.Ct. 2720, 2727, 53 L.Ed.2d 786 (1977) (“If the employer discerns fallacies or deficiencies in the data offered by the plaintiff, he is free to adduce countervailing evidence of his own.”); Segar v. Smith, 738 F.2d at 1267-68. We hasten to observe that, as the Supreme Court has stated, “statistics are not irrefutable.” Teamsters, 431 U.S. at 340, 97 S.Ct. at 1856. After plaintiffs put on a statistical case, it remains open on rebuttal for defendants to rely on all types of evidence, statistical and otherwise. In the typical case, defendants’ rebuttal case will likely focus on (1) inadequacies in the plaintiffs’ statistical case, (2) an alternative, more favorable statistical case, or (3) a non-discriminatory explanation for the statistical disparities. Since the ultimate burden of persuasion rests always with plaintiffs, see United States Postal Serv. Bd. of Governors v. Aikens, 460 U.S. 711, 716, 103 S.Ct. 1478, 1482, 75 L.Ed.2d 403 (1983); Segar v. Smith, 738 F.2d at 1284, district courts must weigh in the balance all the evidence — both plaintiffs’ statistical proof and defendants’ rebuttal — in reaching the ultimate conclusion as to liability. Again, we draw from the Supreme Court’s teaching: Whether ... a [statistical] analysis does carry the plaintiffs’ ultimate burden will depend in a given case on the factual context of each case in light of all the evidence presented by both the plaintiff and the defendant. However, as long as the court may fairly conclude, in light of all the evidence, that it is more likely than not that impermissible discrimination exists, the plaintiff is entitled to prevail. Bazemore v. Friday, 478 U.S. 385, 106 S.Ct. 3000, 3009, 92 L.Ed.2d 315 (1986) (per curiam) (Brennan, J., concurring for a unanimous Court on this point) (emphasis added). B. Plaintiffs’ Statistical Challenge to the Union's Educational Prerequisite to the Journeyman Exam In light of the governing legal framework, we turn again to the case at hand. At bottom, plaintiffs claim that (1) unneces *1414 sary barriers to taking the journeyman 9 exam prevented (or delayed) the entry of otherwise qualified workers into Union ranks, and (2) those barriers disproportionately disadvantaged black rodmen. The proportion of eligible blacks who became Union members, plaintiffs contend, is much lower than the proportion of eligible whites who did. Inasmuch as the high school diploma requirement is no longer part of the case, see supra Part III.C., 10 the employment practices we are called on to consider are two: the Apprenticeship Program and the Training Program. It bears emphasis that plaintiffs’ challenge is simple and direct: An educational prerequisite — either Apprenticeship or Training — discrimina- torily delayed union membership for qualified black permit workers. According to plaintiffs the educational prerequisite is utterly unnecessary if one can pass the journeyman exam. Under this theory, since those workers who are sufficiently experienced to take (and pass) the exam without undergoing an educational program are disproportionately black, delaying membership by means of such a program is unlawfully discriminatory. 1. The Experienced Pool Analysis To prove that the Union’s 11 educational prerequisite to the journeyman’s exam is discriminatory, plaintiffs were required to demonstrate that during the period in question the percentage of eligible blacks who became Union members — i.e., took and passed the journeyman exam— was significantly lower than the percentage of eligible whites. To accomplish this, plaintiffs relied on an expert in labor economics, Professor Sheldon Haber, to construct a statistical model, which he dubbed the “experienced pool” analysis. Plaintiffs counted and identified as to race both potential and actual journeyman examinees, and compared the racial composition of the two groups. Complicating the analysis was the fact that the Union does not keep statistics regarding applications to take the exam; 12 thus, a proxy for identifying potential applicants had to be devised. One important fact was deemed to be of especial relevance in crafting a proxy. During the 1971 Open Period, the Union itself relied on two years’ experience as the criterion for determining who was qualified to take the journeyman exam. In identifying a proxy for potential applicants, Professor Haber therefore took two years as the benchmark for sufficient experience to take the exam. With this benchmark in hand, Haber sought to identify non-member permit workers with at least two years’ experience in order to determine the pool of “likely examinees.” This pool was then compared to the pool of workers who actually took the exam, who were referred to as “actual examinees.” Another complication arose, however, in completing the analysis: Union pension records reflect workers’ experience in terms of hours, not years. In consequence, Professor Haber had to calculate (or estimate) the number of hours that closely approximates two years’ experience in the rodman trade. To determine this figure, Haber referred back to the examinees during the Open Period in 1971, and calculated the average number of hours worked by those examinees in the two years (1969 and *1415 1970) prior to the Open Period. Professor Haber then calculated three averages: one for whites, one for blacks, and a combined white and black workers average. With these three averages, he chose the lowest average figure of 2150 hours (for whites) as the benchmark. This conservative methodology assured that the pool of likely examinees would not be skewed in favor of blacks. 13 Plaintiffs then determined the percentage of workers with 2150 hours of experience who took the entrance exam (almost all of whom passed, and therefore became Union members, see infra n. 15). 14 For the three-year period prior to the filing of this lawsuit (October 22, 1972 through October 21, 1975), the proportion of experienced whites who became Union members was 33.6 percent (49 out of 146); however, the proportion of experienced blacks who became members was a much lower 15.3 percent (19 out of 124). See Tr.F. 82; see also Brief of Appellees at 63. 15 The possibility that a difference of this magnitude would occur by chance is approximately one in 1000, well over the requisite two standard deviations. 16 See Tr.F. 82. Plaintiffs also introduced evidence relating to Union admissions going back to 1967, all of which showed a statistically significant disparity between the proportion of eligible blacks and whites who became Union members. See id. Dr. Haber’s experienced pool analysis thus showed that the difference in the proportion of eligible white and black achievement of Union membership far surpassed the five percent significance level. The District Court concluded, accordingly, that plaintiffs had established a prima facie case of racial discrimination. Tr.F. 81. The burden of rebutting the prima facie case then shifted to defendants. C. Defendants’ Objections to Plaintiffs’ Statistical Case As in the District Court, defendants launch several broad attacks on plaintiffs’ statistical case. At least one contention, namely that Professor Haber was not a credible witness, can readily be disposed of. Credibility determinations are obviously for the trial court to make; our function on appeal is inconsistent with revisiting the credibility of an expert witness unless his testimony was “patently unsound.” 9 C. Wright & A. Miller, Federal Practice and Procedure § 2586, at 740 (1971). We are unpersuaded that Professor Haber’s testimony can fairly be dismissed on the basis *1416 of that daunting standard. However, defendants’ other arguments merit fuller treatment. 1. The Nature of Defendants’Burden on Rebuttal As we indicated above, to demonstrate that statistical evidence is invalid, the challenger must present “credible evidence that the statistical proof is defective” and “a plausible explanation of how the asserted flaw is likely to bias the results against his or her position.” Palmer v. Shultz, 815 F.2d 84, 101 n. 13 (D.C.Cir.1987) (quoting D. Baldus & J. Cole, Statistical Proof of Discrimination vii (1986 Supp.)). In Bazemore v. Friday, 478 U.S. 385, 106 S.Ct. 3000, 3009, 92 L.Ed.2d 315 (1986) (per curiam), Justice Brennan, concurring for a unanimous Court on this point, stated: [I]t is clear that a [statistical] analysis that includes less than “all measurable variables” may serve to prove a plaintiffs case. A plaintiff in a Title VII suit need not prove discrimination with scientific certainty; rather, his or her burden is to prove discrimination by a preponderance of the evidence. To rebut, the challenger must adduce proof specifically showing that an alleged defect actually biases the results. Mere conjecture or general assertions of inadequacies in the opponent’s statistical case, without demonstrating their effect on the results, will not suffice. Palmer v. Shultz, 815 F.2d at 101 (discussing Bazemore’s “dictates”). 17 With this additional background, we turn to defendants’ specific attacks on plaintiffs’ prima facie statistical case. 2. Defendants’ Objections to Plaintiffs’ Statistical Results Defendants argue that the experienced pool analysis is so flawed and divorced from reality as to be meaningless. Their challenges are several. According to defendants, the chosen benchmark of 2150 hours did not represent the cumulative experience of the Open Period examinees, but rather their average hours for the two pri- or years. Thus, the actual experience of the Open Period examinees most likely exceeded 2150 hours by a large margin. Defendants argue that this inaccuracy renders the experienced pool analysis useless, because 2150 hours has no basis either as a measure of the actual experience relied on by the Union during the Open Period, or as an objective approximation of the amount of experience which qualifies one to take the exam. This asserted shortcoming in the experienced pool analysis, however, biases the results in defendants’ favor. Professor Haber testified that he purposely chose the lower (white) average in order to maximize the number of whites in the pool. 18 According to defendants themselves, “the lower the ‘benchmark,’ the lower the proportion of blacks in the ‘experienced pool.’ ” Brief of Local 201 at 106. Given the unmanipulable nature of the figure of actual new members, the ultimate percentage of eligible workers selected for Union membership depends entirely on the number of individuals in the eligible pool: the more blacks in the pool of “likely examinees,” the lower the percentage of black “actual examinees” as a proportion of black “likely examinees” will be, and vice versa. Because white non-members on average had worked fewer hours than black non-members, a lower benchmark increases the number of white “likely examinees” relative to the number of black “likely examinees.” The respective percentages of “likely examinees” who became “actual examinees,” it follows, are correspondingly lower for whites and higher for blacks. Thus, rather than demonstrating that the 2150 hour benchmark biases the results in favor of plaintiffs, defendants’ analysis suggests exactly the opposite. *1417 Defendants also argue that the failure to segregate the experienced pool by age (that is, to analyze separately the group over age 30 and the group under age 31) fatally skewed the results in favor of plaintiffs. Defendants maintain that there was no reason not to segregate by age when available data made it possible to do so; this failure is significant, they argue, because the respective paths to Union membership in the Apprenticeship and Training contexts were so different. Defendants maintain that in the under-31 group, blacks as a proportion of the total experienced pool constituted 24.8 percent (the black “availability rate”), while black participation in the Apprenticeship Program was 30.3 percent, a figure obviously greater than the black “availability rate.” See Brief of Local 201 at 98. Similarly, in the over-30 pool, blacks constituted 75.8 percent of the experienced workers, with their participation rate in the Training Program at 96.2 percent, again a figure well above the black “availability rate.” Id. Defendants maintain that the failure to segregate the experienced pool analysis by age therefore skewed the results in plaintiffs’ favor. This argument suffers from a fatal flaw. Defendants’ analysis focuses on black participation in the Apprenticeship and Training programs, rather than black completion of the programs (i.e., achievement of Union membership). If one focuses on black participation as a whole — not segregating by age, the asserted flaw in plaintiffs’ analysis — the results are also favorable to defendants. Thus, the failure to segregate by age had no independent demonstrable effect on the validity of the experienced pool analysis. This suggests that defendants’ challenge to plaintiffs’ statistical case is in fact an attack on the premises underlying the statistical model, to which we now turn. 3. Defendants’ Attack on the Premises of the Experienced Pool Analysis Defendants attack several fundamental aspects of the experienced pool analysis. Among their objections are: (1) that the concept of “access” to the exam relied on by plaintiffs is flawed; (2) that not all experienced rodmen, i.e., “likely examinees,” were interested in becoming journeymen; (3) that no specific procedure within the Apprenticeship or Training Program was shown to be discriminatory; (4) that the Union cannot be forced to increase the size of its membership in order to achieve racial balance; and (5) most centrally, that the experienced pool did not account for “minimum objective qualifications” of the trade because an educational prerequisite is, and always has been, uniformly required. (a) The “False” Concept of “Access” First, defendants argue that it is wrong to regard only those workers who completed one of the educational programs and took the exam as having "access” to the exam. Rather, they maintain, the proper definition of “access” to membership includes those who were admitted to either the Apprenticeship or Training programs. As defendants see it, the only “requirement” to gain access to Union membership is to secure admission to one of the two educational programs; no one “fails” or is otherwise forced out of either program, as evidenced by the fact that virtually all who finished their respective program passed the exam. To survive the educational component of either program, defendants maintain, all one needed to do, in effect, was show up for class. Therefore, the real source of disparity in minority membership, the argument goes, is the disproportionate number of minority dropouts from the Apprenticeship Program and, especially, the Training Program. According to defendants, those who chose not to complete one of the educational programs had no less access to Union membership than did their colleagues who diligently completed their particular programs. If we accepted defendants' invitation to focus on the rate of participation in the educational programs, rather than the rate of completion, then plaintiffs’ prima facie case would indeed disappear. Defendants are correct that the racial disparity in admissions to Union membership can be ex *1418 plained entirely by the disproportionate rate of minority dropouts from the educational programs. 19 In defendants’ view, it follows that, inasmuch as there were no allegations of discrimination in the administration of the programs, the experienced pool analysis is of no relevance in determining the ability of minorities to gain Union membership. With all respect, the Union’s focus on participation in the educational programs misses plaintiffs’ fundamental point. Plaintiffs challenge the very existence of a training program as a discriminatory barrier to Union membership. So viewed, the higher dropout rate for blacks obviously buttresses plaintiffs’ case: Absent rebuttal, the fact of disproportionately high minority dropouts demonstrates the effectiveness of the barrier to membership represented by Local 201 ’s educational requirements, particularly the Training Program. Defendants are thus fundamentally in error in grandly asserting that plaintiffs cannot “simply cite the requirement of training as the discriminatory practice at issue.” Brief of Local 201 at 97 n. 106. The requirement of “training” is precisely the issue. See infra Part IV.C.3.e. (b) The Assumption That All Experienced Workers Desired Union Membership Defendants contend, next, that the experienced pool analysis is inadequate because it assumes that all experienced workers desired to become Union members. According to defendants, the record demonstrates that experience does not necessarily make one a “likely examinee.” During the early 1970s, permit workers and journeymen alike were fully employed. In those circumstances, there was little incentive for a rodman to undergo the considerable inconvenience (and expense) of becoming a Union member. Indeed, several of the named plaintiffs chose to forgo opportunities for training which would have led to Union membership. See Brief of Local 201 at 93. Defendants urge that the experienced pool analysis is therefore flawed by virtue of this unfounded assumption. To hold to the contrary, they maintain, would be to require the Union somehow to force workers to join the Union in order to achieve racial balance, a result that is indisputably not required (and indeed forbidden) by Title VII. See Brief of Local 201 at 94. We can safely assume that, for one reason or another, some experienced workers did not desire Union membership. 20 But it does not follow that the experienced pool analysis is thereby rendered inadequate, or that the Union is somehow being required to force workers to join in order to achieve racial balance. Rather, we believe defendants demand more than the law requires from plaintiffs’ statistical case. As a theoretical matter, the experienced pool analysis is not undermined by the (partially) inaccurate assumption that experienced workers were “likely examinees.” The reason is this: There is no reason to assume that blacks were as a general matter less interested in Union membership than whites. Certainly, defendants have presented no persuasive arguments or evi *1419 dence to the contrary. Indeed, during the Open Period, when blacks and whites had equal opportunity to take the exam, they did so in relatively equal proportions. Absent a showing that the demonstrated inadequacy in the experienced pool analysis biased the results in plaintiffs’ favor — that is, that black nonmembers did not desire to be members in roughly equal numbers as whites — defendants fail to undermine the prima facie case. (c) The Failure to Identify Specific Discriminatory Procedures, or to Demonstrate that Defendants’ Conduct Caused the Racial Disparities Defendants next urge that plaintiffs failed to identify the specific test, procedure or practice alleged to have had a discriminatory impact, or (under a disparate treatment or section 1981 analysis) to demonstrate that discrimination was the Union’s “standard operating procedure.” See Brief of Local 201 at 94-96. Defendants argue that a prima facie case discrimination was therefore not made out. These arguments can be dealt with in short order. Quite simply, defendants once again decline to recognize the thrust of plaintiffs’ challenge. The "specific procedure” under challenge is the requirement of classroom training before experienced workers may qualify to enter the ranks of journeymen rodmen. That theory of the case fully satisfies defendants’ obvious right to know precisely what is under challenge. And defendants have failed to explain why the asserted barrier of an absolute educational requirement, regardless of experience and ability, is somehow shielded from attack. With respect to the alleged failure to demonstrate that discrimination was the Union’s “standard operating procedure,” plaintiffs’ statistical proof, reaching the requisite showing of approximately two standard deviations, supplies an inference of discriminatory intent for the reasons set forth in Part IV.A.l. of this opinion. Defendants counter that there has been no showing of a causal connection between the challenged practice and the alleged discriminatory result. According to defendants, “[t]he Court cannot indulge in the assumption that Defendants caused people to drop out of the apprentice or training programs." Brief of Local 201 at 96. Defendants argue that no evidence suggested, much less demonstrated, that the higher minority dropout rate from the two programs was attributable to any of their actions. Here too, defendants have missed a basic point, which we have already elucidated: in a case based on statistical proof, direct evidence of discrimination is unnecessary. See Hazelwood School Dist. v. United States, 488 U.S. 299, 807-08, 97 S.Ct. 2736, 2741, 53 L.Ed.2d 768 (1977); Segar v. Smith, 738 F.2d 1249, 1277-79 (D.C.Cir.1984), cert. denied, 471 U.S. 1115, 105 S.Ct. 2357, 86 L.Ed.2d 258 (1985). Indeed, the entire notion of employing statistical proof is to eliminate non-discriminatory causes as likely explanations for racial disparities. In the present context, it seems to us that as a matter of logic there are four possible explanations to account for the failure of blacks to gain Union membership in equal proportions to whites: a) pure chance; b) blacks did not desire to join the Union in roughly equal numbers as whites; c) blacks failed the exam in greater percentages than whites; and d) the educational prerequisite discouraged blacks from taking the exam in greater proportion than whites. Possibility (a) was, of course, eliminated as part of plaintiffs’ prima facie statistical case. Possibility (b) can readily be eliminated since, as discussed above, there is no reason to assume that blacks in general had less desire than whites to join the Union. (Indeed, as we saw above, the evidence as to the Open Period suggests exactly the opposite). Possibility (c) is untrue as a matter of fact, as the parties agree. That being so, plaintiffs by their statistical proof established a prima facie case that possibility (d) provides the true explanation. Under settled principles, the burden thereupon shifted to defendants to demonstrate to the contrary. Defendants are therefore off the mark in arguing that plaintiffs have not shown causation. Contrary to defendants’ protestations, the burden fell to them to show that some racially neutral explanation existed for why blacks *1420 were failing, disproportionately, to become Union members. (d) The Experienced Pool Analysis Would Require the Union to Maximize its Membership Ranks to Achieve a Racial Balance Defendants argue that the experienced pool analysis operates so as to penalize the Union for not maximizing its membership ranks to achieve racial balance. See Brief of Local 201 at 103-05. According to defendants, the largest portion of the experienced pool consisted of workers over age 30; this group also happened to be disproportionately black. Defendants reason that because the Training Program was an affirmative action program, and whites over age 30 therefore had less effective avenues to Union membership than did blacks, plaintiffs’ complaint boils down to a quibble that greater numbers of blacks over age 30 were not admitted to Union ranks. And, defendants continue, the only reason for admitting these more experienced workers would be to achieve a desired racial balance. According to defendants, Title VII does not require them to achieve a racially balanced membership. To be sure, defendants are correct that unions have a legitimate, racially neutral interest in limiting the size of their memberships in accord with market demands. No one in this case has quarreled with the proposition that, at least insofar as the civil rights laws are concerned, Local 201 should be permitted to continue to “determine[] its number of apprentice and trainee indentures based on available employment.” Brief of Local 201 at 105. But it is equally clear that Unions are not permitted to limit their rolls in a discriminatory manner. Plaintiffs do not claim, and we emphatically do not hold, that the Union’s vice was in failing to open its doors to all experienced blacks over the age of 30. 21 Rather, we hold today only that the means chosen by the Union to achieve its legitimate end of limiting membership were, in the face of plaintiffs’ proof, impermissibly discriminatory. The Union remains at liberty to employ a more stringent exam, or any other job-related system of qualifying workers for Union membership, so long as the result is not violative of the civil rights laws. (e) The Experienced Pool Analysis Did Not Account For Minimum Objective Qualifications Defendants’ final challenge to the plaintiffs’ prima facie case is fundamental in nature. It is well established that if a statistical model does not take into account the legitimate, objective qualifications for the jobs being analyzed, then it fails sufficiently to focus on an appropriate labor pool, and is therefore deficient in establishing a prima facie case. See Palmer v. Shultz, 815 F.2d 84, 91 n. 6 (D.C.Cir.1987); Segar v. Smith, 738 F.2d 1249, 1274 (D.C.Cir.1984), cer t. denied, 471 U.S. 1115, 105 S.Ct. 2357, 86 L.Ed.2d 258 (1985). According to defendants, the experienced pool analysis, in assuming that experience alone can qualify one to be a journeyman, fails to account for minimum objective qualifications for becoming a Union member. Defendants argue that plaintiffs’ statistical proof therefore failed to establish a prima facie case. At first blush, defendants’ argument appears formidable. A basic premise of the experienced pool analysis, and indeed of plaintiffs’ entire case, is that the Apprenticeship and Training programs are unnecessary for some workers, namely those sufficiently experienced to pass the rodman exam without classroom training. But it is undisputed that the rodman trade has historically been apprenticeable; moreover, it stands to reason that on-the-job experience alone may not necessarily teach all that a fully qualified rodman should know. Nonetheless, although there was conflicting testimony at trial, the District Court was unsatisfied that the Training Program classes to which plaintiffs were subjected were in *1421 fact substantive in nature or that workers learned through attendance at such classes. 22 But there is another factor as well. During the 1971 Open Period, the Union admitted workers to the exam based entirely on experience at the trade. See Tr. 1484 (vol. h), 1563-64 (vol. i) (testimony of Mr. Grigsby, Local 201’s Business Manager). All workers who were not journeymen members with at least two years’ experience — the approximate length of the apprenticeship period — were invited by the Union to take the exam during that period. It was this very amount of experience, on which the Union itself had relied in the past, that plaintiffs employed as the minimum necessary to qualify for the exam in constructing the statistical case. In our view, the existence of the Open Period points to the conclusion that the Union itself has not viewed an educational requirement as an absolute, minimum objective qualification for becoming a journeyman rodman. We do not doubt that the Union could reasonably conclude that apprenticeship or training is preferable to experience alone in identifying and choosing journeymen rod-men. As we have said earlier, absent discriminatory practices, the Union remains free to utilize any such job-related vehicles. But the Union has, in effect, hoisted itself on its own petard, having chosen in the Open Period to treat experience alone as sufficient for admission to the journeyman exam. It therefore cannot now be heard to complain that classroom training was, all along, absolutely indispensable. Recognizing the vulnerability posed by the Open Period, defendants respond that that episode was an isolated, short-term event, a one-time practice imposed by the International. Moreover, they protest, the exam utilized during that brief period was different from the normal journeyman’s exam, with the concomitant result that workers failed the exam in high numbers. We have no quarrel with these asserted facts, but we disagree with the Union as to their significance. 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. We hasten to add that there is nothing remarkable in our rejecting defendants’ argument with respect to minimum objective qualifications. We in no wise disparage the legitimate qualifications for becoming a journeyman rodman, see Griggs v. Duke Power Co., 401 U.S. 424, 436, 91 S.Ct. 849, 856, 28 L.Ed.2d 158 (1971); nor do we in any manner suggest that the Union is required to admit unqualified individuals, see Local 28, Sheet Metal Workers Int’l Ass’n v. EEOC, 478 U.S. 421, 106 S.Ct. 3019, 92 L.Ed.2d 344 (1986). Under our analysis, the Union remains free, among other things, to (1) require significant rodman experience before an applicant may be admitted to the journeyman exam, (2) offer (cured of discrimination against experienced workers) both the Apprenticeship and Training programs, and (3) devise a more exacting or thorough exam for rod-men 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). D. Defendants’ Rebuttal Case Defendants’ various objections to plaintiffs’ statistical case are best considered as an effort to undermine the validity of the experienced pool analysis. The record is, indeed, devoid of any affirmative rebuttal case — that is, seeking to prove by their *1422 own evidence that admission to Union ranks was not racially disproportionate. We therefore conclude, in light of our earlier analysis, that plaintiffs’ prima facie case went unrebutted. The Union is thus liable to those class members who were experienced workers, but were delayed entry to Union ranks by the particular educational prerequisite affecting them from the end of the Open Period until the filing of suit on October 21, 1975. 23 E. Plaintiffs’ Failure to Show a Pattern of Discrimination The District Court stated broadly that “plaintiffs ... demonstrated that, since 1967, all of the rules used by the defendants for selecting examinees have discriminatorily prevented blacks from gaining membership in [the Union],” Tr.F. 82, and that these “discriminatory actions against plaintiffs and the class are continuing violations of Title VII and section 1981.” Trial Conclusion of Law (“Tr. C.”) 22; see also Tr. C. 21 (“The evidence presented demonstrates persistent, pervasive and intentional discrimination against black rod-men.”) The District Court thus found defendants liable for all selection procedures used since 1967, under a theory of continuing violation or pervasive pattern of discrimination. See Milton v. Weinberger, 645 F.2d 1070, 1074-75 (D.C.Cir.1981) (referring to continuing violations as “series of related acts, one or more of which falls within the limitations period, or the maintenance of a discriminatory system both before and during the statutory period” (quotation and citations omitted)); United Air Lines, Inc. v. Evans, 431 U.S. 553, 558, 97 S.Ct. 1885, 1889, 52 L.Ed.2d 571 (1977); Valentino v. United States Postal Serv., 674 F.2d 56, 65-66 (D.C.Cir.1982). Plaintiffs’ theory is that, over many years, the Union erected a series of barriers which, in succession, accomplished the discriminatory purpose of keeping blacks out of the Union. In plaintiffs’ view, the various selection systems chosen by the Union, taken together, reflect an insidious pattern: “deny access to an exam, allow access to an exam but fail blacks disproportionately, then deny access again.” Brief of Appellees at 29. Plaintiffs hope to connect the violations which are clearly within the limitations period — the delay inherent in requiring experienced workers to undergo apprenticeship or training — to the violations we have held to be outside the limitations period — the allegedly discriminatory Open Period exam and the allegedly discriminatory high school diploma requirement. The District Court agreed with plaintiffs and held defendants liable for all the alleged violations. Under settled principles, the appropriate analysis with respect to continuing violations focuses on whether the current violations were taken pursuant to the same employment policy as the actions sought to be challenged outside the normally applicable limitations period. United Air Lines, Inc. v. Evans, 431 U.S. 553, 558, 97 S.Ct. 1885, 1889, 52 L.Ed.2d 571 (1977); Laffey v. Northwest Airlines, Inc., 567 F.2d 429, 473 (D.C.Cir.1976), cert. denied, 434 U.S. 1086, 98 S.Ct. 1281, 55 L.Ed.2d 792 (1978). The inquiry is thus whether the various admission procedures since 1967, taken together, constituted a single policy to discriminate. For reasons which we will explain below, we hold that they do not. Based on the entire record, we are unpersuaded that the totality of the Union’s selection procedures constitute a “pattern of discrimination,” McKenzie v. Sawyer, 684 F.2d 62, 73 (D.C.Cir.1982), or “a chain of connected events,” Bethel v. Jefferson, 589 F.2d 631, 636 (D.C.Cir.1978), sufficient to justify relaxing the normal limitations periods for challenging those practices. Indeed, plaintiffs have introduced no evidence connecting the various procedures so as to establish an ongoing policy and plan to discriminate. First and foremost, the Open Period procedure marked a sharp break in the Union’s traditional admission practices. Sud *1423 denly, any individual with the requisite level of experience was permitted access to the exam. Thereafter, the new system instituted at the conclusion of the Open Period likewise broke any connection to prior selection practices. It manifestly represented a break from the Open Period. We cannot fail to note that the Training Program, instituted after the Open Period, was a federally funded, approved, and supervised, affirmative action program. The dual Apprenticeship/Training system was thus an entirely novel system, unconnected to the Open Period procedure or to the earlier Executive Board/Apprenticeship system. Absent any evidence of intent to exclude blacks over time in the fashion plaintiffs hypothesize, the various systems are more naturally and reasonably viewed as separate. There certainly has been no showing that the Union long ago conceived a plan to exclude blacks by whatever means seemed efficacious as time progressed. Accordingly, the District Court’s findings to the contrary are reversed. V. Plaintiffs’ Allegations of Retaliatory Conduct Under Title VII The District Court found that the defendants “or other agents” not further identified unlawfully retaliated against plaintiffs Jackson, Kirkland, Berger, Lewis, and Bellamy in violation of section 704(a) of Title VII, which makes it an unlawful employment practice for an employer to discriminate against any of his employees or applicants for employment, for an employment agency, or joint labor-management committee controlling apprenticeship or other training or retraining, including on-the-job training programs, to discriminate against any individual, or for a labor organization to discriminate against any member thereof or applicant for membership, because he has opposed any practice made an unlawful employment practice by this subchap-ter, or because he has made a charge, testified, assisted or participated in any manner in an investigation, proceeding, or hearing under this subchapter. 42 U.S.C. § 2000e-3(a). To establish a prima facie case under section 704(a), a plaintiff must show: 1) that he or she engaged in activity protected by the statute; 2) that the employer, joint labor-management committee, or labor organization engaged in conduct having an adverse impact on the plaintiff; and 3) that the adverse action was causally related to the plaintiff’s exercise of protected rights. Mitchell v. Baldrige, 759 F.2d 80, 86 (D.C.Cir.1985); McKenna v. Weinberger, 729 F.2d 783, 788, 790 (D.C.Cir.1984). Once that burden has been met, the defendant may introduce rebuttal evidence providing legitimate, nonretaliatory reasons for its conduct. The plaintiff may then attempt to show that the defendant’s asserted justification is “merely a ‘pretext’ covering up unlawful retaliation through the guise of innocent business planning.” Williams v. Boorstin, 663 F.2d 109, 116 (D.C.Cir.1980). The evidence presented by the parties may at this point suggest that the reasons for the defendant’s conduct are mixed, consisting of both retaliatory and legitimate factors. For that reason, this circuit has adopted a “but for” test of causation: “If the plaintiff has made a showing of ‘pretext,’ the defendant ... must then demonstrate by clear and convincing evidence that the plaintiff would have [been subject to the defendant’s actions] anyway absent retaliation for the plaintiff’s participation in protected conduct.” Id. at 117. The District Court held that each of the plaintiffs had established a prima facie case of retaliation. Tr.C. 29. In addition to specific findings relating the adversity each of the plaintiffs had suffered, the court made two additional, but very general, findings. First, the court found that “[t]here is overwhelming evidence that defendants and their agents knew of plaintiffs’ participation in this suit or in otherwise protected conduct.” Tr.C. 28. Second, the court rejected the unspecified justifications the defendants had offered, apparently regarding them as pretextual. Tr. C. 29. For reasons we discuss below, we find that with one exception the District Court’s findings of retaliation are clearly erroneous. A. Plaintiffs Berger and Lewis The court’s findings respecting plaintiffs Berger and Lewis share common *1424 features; in both instances, the District Court found that the plaintiffs had been subjected to oral threats after they participated in this lawsuit. The court found that “Berger heard Tommy Gilmer, then business agent for Local 201, state at a union membership meeting ... that he was going to make it hard on those who filed this suit.” Tr.F. 113. The court also found that Gilmer threatened to withhold from Lewis an application for the Training Program until Lewis agreed to drop his charges of discrimination. Tr.F. 114. In neither case, however, did the District Court find that the “threat” was carried forward. In the absence of a finding that the plaintiff has suffered adverse action, a retaliation claim fails as a matter of law. Evans v. Davie Truckers, Inc., 769 F.2d 1012, 1014 (4th Cir.1985). The District Court made no specific findings that Berger or Lewis were subject to adverse treatment, and we cannot agree that Gilmer’s statements, standing alone, can reasonably be viewed as “veiled threats and harassment” amounting to “classic examples of ‘retaliation.’ ” Tr.C. 27. Our review of the record, in fact, reveals that Jackson himself testified that Gilmer did not threaten to withhold the Training Program application from him, but merely asked Lewis if he would drop the charges of discrimination once he was accepted into the program. 24 Similarly, Gilmer’s statement that “he was going to make it hard” on the plaintiffs, though probative of retaliatory animus, had no effect itself on Berger, and was not put into effect through any action against Berger; it can best be characterized as “ill-advised but essentially harmless.” Reese v. Batesville Casket Co., 25 Fair Empl.Prac.Cas. (BNA) 1472, 1477 (D.D.C. 1981) [Available on WESTLAW, 1981 WL 176]. Because the District Court’s findings lack an essential ingredient of a retaliation claim, they are insufficient to support its judgment against the defendants. We recognize, however, that repeated threats against individuals in response to their exercise of protected rights may amount to harassment sufficient to establish a claim of retaliation. See Rogers v. McCall, 488 F.Supp. 689, 697 (D.D.C.1980); B. Schlei & P. Grossman, Employment Discrimination Law 554 (2d ed. 1983). For that reason we have reviewed the record with particular care for any evidence of repeated threats or other individualized harm to either Berger or Lewis that can fairly be reregarded as retaliatory. See Reese, 25 Fair Empl.Prac.Cas. at 1477. That search, however, has been fruitless. 25 The judgment of the District Court concluding that plaintiffs Berger and Lewis had suffered unlawful retaliation at the hands of appellants is, therefore, reversed. B. Plaintiff Jackson The District Court found that plaintiff Jackson “was laid off in January 1975, after charges of discrimination had been filed with the [EEOC], and was told by the superintendent of the job site that he had orders from [a former Local 201 official] to fire him.” Tr.F. 111. Jackson’s testimony is the only evidence of the Union’s (or any other defendant's) participation in his layoff, and the portion of his testimony that makes this connection was, upon objection, excluded from the record by the District Court. Tr. at 249-50. The only record evidence bearing on the circumstances surrounding Jackson’s layoff and the involvement of the defendants therein is the testimony of the same superintend *1425 ent whom Jackson alleges made the statements implicating Local 201. That superintendent — himself a member of the plaintiff class — testified that Local 201 was not involved in Jackson’s layoff. Tr. at 2543. Because there is no competent evidence linking any of the defendants to Jackson’s layoff, the District Court’s finding is clearly erroneous. Even if we were to accept Jackson’s proffered testimony, the District Court’s finding would remain unsound. Jackson testified that the reason for his layoff was because he was black, Tr. at 250, and because the Union “found out [he] was making $24,000 a year [and] that that is too much for a permit man, especially [a] black [one].” Id. at 279. Clearly, Jackson does not view himself as a victim of retaliatory conduct; in fact, nowhere in his testimony is the charge filed with the EEOC mentioned, much less connected with his layoff. Read in the light most favorable to the plaintiff, Jackson’s testimony at most suggests that he was discriminated against on the basis of race. It is simply irrelevant to a charge of retaliation, 26 It is apparent that the District Court confused the standards applicable to claims of retaliation with the standards applicable to claims of racial discrimination. Whatever merit Jackson’s claim may have under Title VII’s provisions prohibiting racial discrimination in employment, that is not the claim before us. The court’s conclusion that Jackson was laid off in retaliation for the exercise of protected statutory rights is reversed. C. Plaintiff Kirkland The District Court found that plaintiff Kirkland had been laid off in retaliation for participating in this lawsuit. Tr. F. 112. The layoff occurred approximately one week after a conversation between Kirkland and his supervisor, Ray Coda, in which Coda questioned Kirkland about the lawsuit. Although Kirkland’s testimony thus establishes the essential elements of a retaliation claim against his employer — i.e., engaging in protected activity, an adverse employment action, and knowledge of the protected activity on the part of the employer — that employer was not named as a defendant in this case. section [§ 704(a) ] relates solely to discrimination against an applicant or employee on account of his participation in legitimate civil rights activities or protests, while [section 703(a)(1) of Title VII] deals with the broader and centrally important question under the Act of whether, for any reason, a racially discriminatory employment decision has been made. Our review of the record indicates that there is no evidence linking Kirkland’s layoff with any of the named defendants in this case; nor does the sequence of events leading up to the layoff provide a basis from which an inference could be drawn that the hands of any of the defendants were lent in support of the employer’s actions. We also discern no basis in the record for treating Kirkland’s employer as an “agent” for any or all of the defendants. The plaintiffs argue that Local 201 may nonetheless be held liable for retaliation because it has an affirmative duty to challenge employer discrimination against union members and failed to do so in this case. It is true that the Supreme Court has recently held that a union that ignores or refuses to process its members’ grievances against employers for alleged racial discrimination may be held liable under Title VII and section 1981. Goodman v. Lukens Steel Co., — U.S. —, 107 S.Ct. 2617, 2625, 96 L.Ed.2d 572 (1987). That decision, however, provides no support for the argument here advanced by the plaintiffs. The District Court found that the alleged retaliatory act against Kirkland consisted in the layoff, not in the defendants’ failure affirmatively to oppose the employer’s discriminatory conduct. Tr.C. 27. Thus, whether any or all of the defendants had an affirmative duty to take action against Kirkland’s employer, is an issue that was neither argued before, nor ad *1426 dressed by, the District Court. 27 We therefore hold that the District Court erred in finding the defendants liable for retaliation against Kirkland. D. Plaintiff Bellamy In a letter dated November 11, 1974, plaintiff Bellamy complained to the International about the Union’s discriminatory practices. Shortly thereafter, he was laid off from employment by Y & M Steel. 28 When he next reported to Local 201’s referral hall, a Union official confronted Bellamy about the letter, the two men “exchanged some words,” and the official threatened to pass over Bellamy in making referrals. Tr. at 51. In fact, however, Bellamy obtained employment through the Union the very next day, but only at reduced wages. The Union explained the cut in pay to Bellamy as an incident of his participation in the Training Program. The District Court found that this reduction in wages constituted unlawful retaliation. Tr.F. 115. Having reviewed the record, we conclude that the District Court’s finding is not clearly erroneous. Bellamy’s testimony clearly established a prima facie case of retaliation. We also believe that the District Court could reasonably regard the defendants’ asserted justifications as merely pretextual. The defendants attempt to justify the wage cut under the terms of an agreement Bellamy signed when he entered the Training Program. That agreement — an application form — provided that trainees may be referred to employers at wages below those commanded by journeyman rodmen. Tr. at 2698-2701. Bellamy entered the Training Program sometime in 1973, long before he was laid off. From the time he entered the program until shortly after he wrote to the International, he received full journeyman wages. Thus, while the defendants have presented a potentially legitimate reason for the wage reduction, that reason is not sufficient to explain the timing of the pay cut, nor does it explain why other trainees continued to be referred by the Union at journeyman rates. The defendants’ proffered justification therefore does not satisfy the “clear and convincing” standard under this circuit’s “but for” test of causation. See Williams, 663 F.2d at 117. We therefore affirm the District Court’s judgment that plaintiff Bellamy was subjected to retaliation in violation of Title VII. VI. Liability op the International We have earlier upheld the District Court’s conclusion that the educational pre requisite — i.e., completion of the Apprenticeship or Training Program — as applied to experienced rodmen who wanted to become members of Local 201 had a disproportionate impact on blacks in violations of Title VII and section 1981. Supra Part IV. We have now upheld the court’s finding that plaintiff Bellamy was subjected to unlawful retaliation in the form of reduced wages. Without more, however, these conclusions do not implicate the International. The circumstances under which an international union may be held liable for discriminatory practices of an affiliated local union, or for retaliatory conduct occurring at the local level, is a question of first impression in this circuit. As we explain more fully *1427 below, we have little difficulty concluding that the International’s involvement in the membership practices of Local 201 was sufficiently extensive to subject it to liability under Title VII and section 1981. By contrast, we are unable to discern any basis for subjecting the International to liability for Bellamy’s retaliatory wage reduction. A. Legal Background It has long been established that a collective entity, including a labor organization, “may only be held responsible for the authorized or ratified actions of its officers and agents.” Skimman v. Frank, 625 F.2d 80, 95 (6th Cir.1980) (quoting North American Coal Co. v. United Mine Workers, 497 F.2d 459, 466-67 (6th Cir.1974)). This standard of liability extends generally to situations in which an international union is sued for the conduct of its affiliated local. More specifically, in Section 301(e) of the Labor-Management Relations Act, 1947 (“LMRA”), 29 U.S.C. § 185(e) (1982), which governs suits for violations of contracts between an employer and a union or between two labor organizations, Congress “adopted a common-law agency test” to govern the liability of an international for the acts of its affiliated locals. Carbon Fuel Co. v. United Mine Workers, 444 U.S. 212, 217, 100 S.Ct. 410, 414, 62 L.Ed.2d 394 (1979); see also Shimman, 625 F.2d at 97-99. In Carbon Fuel, the Supreme Court held that in order to hold an international union liable in damages for “wildcat” strikes engaged in by its locals, a plaintiff must adduce specific evidence that the international “instigated, supported, ratified, or encouraged” those actions, id. 444 U.S. at 218, 100 S.Ct. at 414, or “that what was done was done by their agents in accordance with their fundamental agreement of association.” Id. at 217, 100 S.Ct. at 414 (quoting Coronado Coal Co. v. Mine Workers, 268 U.S. 295, 304, 45 S.Ct. 551, 554, 69 L.Ed. 963 (1925)); see also United Mine Workers v. Gibbs, 383 U.S. 715, 735-42, 86 S.Ct. 1130, 1143-47, 16 L.Ed.2d 218 (1966). The plaintiffs argue that the cases in which common law agency principles have been invoked to determine whether an international should be held to account for the activities of a local “have nothing to do with Title VII or section 1981.” Brief of Appellees at 103. True enough. The question is therefore whether any different standard for holding the International liable obtains in this arguably different context. The plaintiffs claim that these civil rights statutes create an “affirmative duty” in the International to eliminate discrimination, such that the International may be held responsible for the discriminatory acts of its local if the plaintiffs demonstrate merely a “sufficient connection” between the International and the discriminatory practices in issue. The primary authority upon which the plaintiffs rely is the Fifth Circuit’s decision in Myers v. Gilman Paper Corp., 544 F.2d 837, modified on other grounds, 556 F.2d 758 (5th Cir.), cert. denied, 434 U.S. 801, 98 S.Ct. 28, 54 L.Ed.2d 59 (1977), which predates the Supreme Court’s decision in Carbon Fuel. In Myers, the court found an international liable for the discriminatory effects of a collective bargaining agreement administered by one of its locals, despite the international’s claim that there was no “specific proof that it caused, participated in, or ratified its local’s acts or omissions.” Id. at 850. The court concluded that a “sufficient connection” existed between the international and the discriminatory practices by virtue of the “close relationship” between the international and the local: Here the international established a close relationship with its locals, under which the international would generally provide advisors who would review and often comment upon the local’s bargaining position. An additional aspect of the relationship was the international’s requirement that locals submit contracts to it for its approval. Id. at 851. While the plaintiffs are certainly correct in arguing that § 301 of the LMRA does not directly control this case, we are convinced that the common-law agency principles underlying it provide the appropriate analytical framework as well under *1428 Title VII and section 1981. Two reasons support this conclusion. First, the Court’s decision in Coronado Coal, which predated the enactment of the original National Labor Relations Act, suggests that where Congress has not otherwise declared the standards governing vicarious liability, a union’s liability for the acts of another is to be determined under common-law agency principles. Second, when Congress adopted a common-law agency standard in the LMRA, it recognized that a local union may in practice enjoy a considerable degree of actual autonomy, despite its formal dependence upon the parent international for its continued existence. See also Boss v. International Bhd. of Boilermakers, 567 F.Supp. 845, 847 (N.D.N.Y.), aff'd, 742 F.2d 146 (2d Cir.1983), cert. denied, 469 U.S. 816, 105 S.Ct. 89, 83 L.Ed.2d 36 (1984). That implicit premise would, of course, apply equally in the context of Title VII and section 1981. Against this background, we think that if Congress intended that international unions be held liable for the failings of their locals with regard to civil rights under a special standard, it would have given some indication to that effect. Moreover, having studied the Fifth Circuit’s decision in Myers, we do not think that the “sufficient connection” test was structured or given content by principles meaningfully distinguishable from common-law agency principles. In Myers, the court found not only that the international and its local had a general “close relationship,” but more important, that the international had in fact “provided an ‘advisor’ to the local in its negotiations and ... approved the resultant collective bargaining agreement.” Id. at 851. Having thus participated in and approved a practice of the local that was later found to be discriminatory in effect, the international would surely have been held accountable for the local’s conduct under the agency standard of the common law, as articulated in Carbon Fuel. We do not believe, therefore, that the “sufficient connection” test, as applied in Myers, supports a less stringent standard of vicarious liability under Title VII and section 1981 than the common-law agency standard that Congress and the Supreme Court have determined is applicable in other contexts. Other Title VII and section 1981 cases in which the “sufficient connection” test has been applied are of no different import; indeed, we believe, that these cases, while speaking of an international union’s “affirmative duty,” confirm our holding that common-law agency principles apply to unions in the civil rights context. In Sinyard v. Foote & Davis Div. of McCall Corp., 577 F.2d 943, 945 (5th Cir.1978), the Fifth Circuit noted that, “[a]s a general proposition ... international labor unions must bear a heavy responsibility in giving effect to the remedial provisions of ... Title VII,” but cautioned that the imposition of any affirmative duty depends “on the relationship between the international and the local and the amount and type of involvement which the international has” with the discriminatory practice under challenge. Id. Citing Myers, the court further noted that, “[t]he precedents on which appellants rely do not sanction our blanket imposition of an affirmative duty on international unions to police their locals to insure nondiscrimination — an undertaking which on occasion may be beyond their capacity.” Id. And although the court endorsed the “sufficient connection” formulation, it applied common-law agency principles to exonerate the international. Thus, the court noted that “the International had not caused or participated in and did not approve the condition complained of.” Id. at 947; see Howard v. International Moulders & Allied Workers Union, 779 F.2d 1546, 1548 (11th Cir.), cert. denied, 476 U.S. 1174, 106 S.Ct. 2902, 90 L.Ed.2d 987 (1986) (international liable where its representative “worked closely” with local negotiators, resulting in discriminatory bargaining agreement); accord Sagers v. Yellow Freight Sys., 529 F.2d 721, 737-38 (5th Cir.1976); see also Kaplan v. International Alliance of Theatrical & Stage Employees, 525 F.2d 1354, 1360 (9th Cir.1975) (international liable where it negotiated and signed discriminatory collective bargaining agreement). *1429 That common-law agency principles apply equally to determine an international union’s liability under the civil rights laws as they do in other contexts is also the unavoidable implication of the Supreme Court’s decision in General Building Contractors Ass’n v. Pennsylvania, 458 U.S. 375, 102 S.Ct. 3141, 73 L.Ed.2d 885 (1982). In that case, the Court declined to impose liability under section 1981 on an employers association for the discriminatory manner in which a union had implemented a collective bargaining agreement that the association had negotiated. The district court had found that the association, by agreeing to the referral system the union administered at its hiring hall, had “delegated” authority to the union to select workers for the association’s employers; it was therefore charged with the “ ‘duty to see that discrimination does not take place in the selection of one’s workforce,’ regardless of where the discrimination occurs.” Id. at 392, 102 S.Ct. at 3150-51 (quoting Pennsylvania v. Local 542, Int’l Union of Operating Engineers, 469 F.Supp. 329, 412 (E.D.Pa.1978)). The Supreme Court, however, found this theory “flawed on its own terms,” declining to sanction the “imposition of liability oh^the employers association] based on the acts of a party with whom it had no agency or employment relationship.” Id. Accordingly, we see no principled reason for dispensing with the requirement of an agency relationship between the International and its local here. Instead, we believe General Building Contractors underscores the need, under Title VII and section 1981, to base one party’s liability for the acts of another party on something more than the abstract and unbounded premise that the entities regulated by those laws have an “affirmative duty” to end discrimination. That something more is to be found in accordance with longstanding agency principles, the “core” of which involves a “ ‘fiduciary relation’ arising from the ‘consent by one person to another that the other shall act on his behalf and subject to his control.’ ” Id. (quoting Restatement (Second) of Agency § 1 (1958)). 29 We do not doubt that a labor organization may in some circumstances have an obligation actively to oppose discriminatory conduct on the part of individuals or entities with which it has no agency relationship, see Goodman v. Lukens Steel Co., — U.S. —, 107 S.Ct. 2617, 2625, 96 L.Ed.2d 572 (1987); Macklin v. Spector Freight Sys., 478 F.2d 979, 989 (D.C.Cir.1973), and our discussion above should not be read as indicating anything to the contrary. Neither Goodman nor any other case, however, suggests that a union’s failure to act in opposition to discriminatory practices of an organization with which it has no agency relationship renders it vicariously liable for that organization’s discriminatory practices; rather, the point of those cases is that the union’s failure to act may be an independent basis for liability under Title VII and section 1981. 30 In this case, therefore, the concerns underlying Goodman and Macklin, and the question whether the International has breached an affirmative duty to oppose the discriminatory practices of Local 201, are inapposite. The plaintiffs did not argue before the district court, and do not argue before this court, that they were discriminated against by the International’s failure to act, in breach of an affirmative duty; rather, they argue that the International is vicariously liable *1430 for the discriminatory conduct of Local 201. Thus, breach of an affirmative duty is not the theory against which the evidence in this case must be measured. The International’s liability depends upon the existence of an agency relationship between the International and Local 201. While we believe that an agency relationship between the International and Local 201 with respect to the particular discriminatory practices in issue is both a necessary and a sufficient basis for holding the International liable under a theory of disparate impact under Title VII, the same conclusion does not follow a fortiori with respect to the plaintiffs’ claims under section 1981. This is because liability can be established without a showing of discriminatory intent under Title VII but not under section 1981. Goodman, 107 S.Ct. at 2622; General Building Contractors, 458 U.S. at 391, 102 S.Ct. at 3150. Thus, we must further determine whether, under section 1981, an agency relationship between the International and Local 201 is sufficient to impute from the local to the International the requisite discriminatory intent. In General Building Contractors, the Court assumed, without deciding, that an organization may be liable under section 1981 for acts of intentional discrimination perpetrated by its agents. See id. at 395, 102 S.Ct. at 3152. Cases in our sister circuits provide no more guidance on the question. In Myers, for example, the court made no distinction between Title VII and section 1981, apparently, but only apparently, thereby deciding that the “sufficient connection” test applies equally to both. Accord Howard, 779 F.2d at 1548. The implication of the Supreme Court’s decisions in Carbon Fuel and Coronado Coal, however, is instructive: in the absence of an explicit congressional directive to the contrary, common-law agency principles govern an international’s liability for the unlawful actions of its locals. Applying those principles under section 1981, we find that at common law a principal may be held liable for the intentional torts of its agent if the agent’s conduct is within the scope of his agency and “if, with knowledge of the conditions, [the principal] intends the conduct, or if he intends its consequences....” Restatement (Second) of Agency § 212 (1958); see id. at § 216. Thus, we hold that an international union may be liable under section 1981 if, with knowledge of the surrounding circumstances, it authorizes, ratifies, or approves a local's actions the effects of which are sufficient to establish a claim of intentional discrimination against the local. With these principles in mind, we turn to the facts that we believe do establish that the International is liable for the central discriminatory conduct in this case. B. International’s Liability for the Educational Prerequisite to the Journeyman Examination In holding the International liable in this case, the district court relied extensively on provisions in the International’s Constitution, finding that these provisions “establishf ] the pervasive authority of the International over the affairs of its affiliated local unions such as Local 201.... In a word, the Constitution identifies and treats affiliated local unions as ‘subordinate bodies.’” Tr.F. 116. As we interpret this finding, the District Court believed that, for purposes relevant here, an agency relationship between the International and Local 201 could be established by merely looking to those terms of the International’s Constitution that govern its relations with its locals. The terms of an international’s constitution can, undoubtedly, provide some evidence of such an agency relationship. See Shimman, 625 F.2d at 97; Boss, 567 F.Supp. at 847, citing Baldwin v. Poughkeepsie Newspapers, Inc., 410 F.Supp. 648 (S.D.N.Y.1976); see also Local Union 984 v. Humko Co., 287 F.2d 231, 241-42 (6th Cir.1961); cert. denied, 366 U.S. 962, 81 S.Ct. 1922, 6 L.Ed.2d 1254 (1961); International Bhd. of Teamsters v. United States, 275 F.2d 610, 612 (4th Cir.1960), cert. denied, 362 U.S. 975, 80 S.Ct. 1060, 4 L.Ed.2d 1011 (1960). To the extent that provisions of the constitution deal specifically with the practices found to be discriminatory, more *1431 over, they may be sufficient in themselves to raise an inference that the local is its agent. In many situations, however, an international’s constitution will paint a misleading picture of the actual relationship it has with its locals. A local that is nominally semi-autonomous may actually be subservient. Alternatively, “a local union may remain autonomous and independent notwithstanding the fact that the International retains a degree of supervisory authority.” Boss, 567 F.Supp. at 847 (citing Baldwin v. Poughkeepsie Newspapers, Inc., 268 F.2d 871 (7th Cir.1958), cert. denied, 361 U.S. 869 (1959)). For this reason, an agency relationship cannot simply be presumed rather than proved; “the diverse situations possible in the varied relationship between parent and local unions make individual examination of the facts, rather than a mechanical application of assumptions, a vital necessity.” Sinyard, 577 F.2d at 947. In that examination, “what should matter is not so much the International’s theoretical control over the local as the nature and extent of actual control.” Shimman, 625 F.2d at 98 n. 36 (citing Hamischfeger Corp. v. Sheet Metal Workers Int’l Ass’n, 436 F.2d 351 (6th Cir.1970)); see also Sinyard, 577 F.2d at 946 (declining to find a “sufficient connection” between an international and its local on the basis of international constitution providing international with “full power” to regulate its locals). In this case, the International’s Constitution indicates that the International had an interest in and potentially a substantial involvement with Local 201’s membership practices. It provides the International with authority to oversee its locals’ membership practices, stating that “[a] copy of every candidate’s application for membership [in an affiliated local] shall be sent to Headquarters for approval_ If a candidate is rejected, the application of such rejected candidate with the reason or reasons for rejection must be sent to Headquarters.” Constitution of the International Ass’n of Bridge, Structural and Ornamental Iron Workers, Art. XXI, § 2. As is usual, membership in the International is ordinarily automatic for anyone admitted to membership in an affiliated local. The International also receives a portion of the initiation fees and monthly dues that each member is responsible for paying to a local. The Constitution does not, however, explicitly require, or authorize locals to require, applicants for membership to complete a Union-supervised educational program. Instead, the Constitution merely requires that, to be admitted to membership, an applicant “must be a practical workman versed in the duties of some branch of the trade ..., of good moral character and competent to demand standard wages.” Id. at Art. II, § 2. Thus, even if we were inclined to give considerable weight to the Constitution standing alone, we would not be compelled to conclude that the International “authorized,” much less directed, the discriminatory practices of Local 201. Looking beyond the terms of the International’s Constitution, however, we find that the International was involved with the membership practices of Local 201 to such an extent that the District Court could infer that the local is the agent of the International with respect to the practices at issue here. First, it is clear that the International believes, and indeed continues to argue, that the rodman trade is an apprenticeable one, requiring extensive classroom training. See Brief of Appellant International at 35-38. The International has thus at all times endorsed the general principle that there should be an educational prerequisite for membership. Second, and more specifically, it is reasonably clear that the International was fully aware of Local 201’s membership policies. According to undisputed record evidence, the International had, on at least one occasion prior to the Open Period, met with Local 201 about membership practices and “discussed at length the reasons why the local should adopt a standard procedure for the acceptance of non-members as well as why nonmembers should be accepted.” Tr.F. 130. Most particularly, the facts could reasonably be viewed by the District Court as establishing that the educational require *1432 ment was a valve regulating access to union membership, which, to a considerable degree, was controlled by the International. Since 1971, there has been only one short-lived departure — the “Open Period” — from the requirement that applicants complete a Union-supervised educational program. The Open Period, during which rodmen having two or more years of experience were allowed to take a special journeyman examination without completing an educational program, was the creation of the International. The local implemented it only on the express instructions of the International, Tr.F. 133, and then only to prevent “future litigation, such as occurred in [other locals.]” Tr.F. 132. After the Open Period ended in June 1971, the International developed and endorsed the Training Program as a replacement for the Open Period’s reliance solely on an examination in admitting experienced rodmen. International President Lyons testified that one of the primary reasons for developing the Training Program was to avoid “diluting” the Apprenticeship Program or creating “a bunch of second-class ironworkers.” Tr. at 3290. With the Training Program, the International “acted to create a vehicle that would bring into [the ironworkers trade] a high percentage of minorities who when they finished this training program would be qualified to earn a living at the iron-workers’ negotiated wage scale.” Tr. at 3298. As applied to inexperienced blacks, the program did indeed open new avenues of opportunity that previously may have been closed; in that respect, the Training Program is to be commended. But in aiming the Training Program broadly at all non-members who were not qualified to enter the Apprenticeship Program, the International endorsed a system that placed unnecessary barriers between experienced black rodmen and Union membership. The International does not really dispute that it played a significant role in establishing the requirement that applicants complete a Union-supervised educational program before being allowed to take the journeyman examination; rather, it attempts to distance itself from these practices by arguing that the decision to establish an Apprenticeship Program or a Training Program remained at all times within the discretion of each local. In addition, the International adamantly insists that it had no control over the day-to-day operation of these programs. These arguments cannot parry the thrust of the plaintiffs’ claim of discrimination. That claim is not that the Training Program or the Apprenticeship Program (setting aside the high school diploma requirement) were themselves discriminatory; rather it is that the requirement that rod-men complete such a program before being allowed to take the journeyman examination worked discriminatory effects. It is this requirement from which the International has not successfully divorced itself. Even if it did not require locals to develop and to administer educational programs, we find ample evidence in the record to support the District Court’s conclusion that the International actively participated in and approved of Local 201’s membership procedures. Tr.C. 30. That is sufficient to establish an agency relationship between the International and Local 201; accordingly, we affirm the court’s judgment holding the International liable under Title VII. We must next consider whether the International had sufficient knowledge of the circumstances prevailing in Local 201, when it participated in and approved the local’s discriminatory practices, to impute to it the intent necessary to establish liability under section 1981. This question need not detain us long, however, because in this case the intent to discriminate may be inferred from the plaintiffs’ statistical showing; the evidence of intent under section 1981 need not be direct. The International’s support of and participation in the very practices to which the plaintiffs’ statistics apply is a sufficient basis from which the intent to discriminate on the part of the International may properly be inferred. In a case based upon direct evidence of the local’s discriminatory intent, it would not necessarily be possible to infer an unlawful intent on the part of the international; a principal may innocently delegate authority to an agent who indepen *1433 dently and unbeknownst to the principal brings an unlawful purpose to its exercise of that authority. This is not such a case, however. C. The International’s Liability for Retaliation Against Plaintiff Bellamy In contrast to the overwhelming evidence of the International’s awareness of and participation in Local 201’s membership practices, there is not a shred of evidence nor any finding by the District Court linking the International to Bellamy’s wage cut. That was a matter purely between Bellamy, the local, and Bellamy’s employer. To find the International liable in this circumstance would impose an unbounded obligation on it to police the actions of its locals, no matter how discrete or spontaneous those actions may be. Because we find no evidence indicating that the International participated in, approved, ratified, or even had knowledge of Bellamy’s wage cut, we reverse the District Court’s judgment holding the International liable for retaliation. VII. Liability of Construction Contractors Council A. Liability Under Title VII Defendant CCC is a multi-employer association that has two undisputed connections with this lawsuit: on behalf of its member employers, it negotiated collective bargaining agreements that govern the referral practices of Local 201, and it appointed trustees to the governing bodies of the Training and the Apprenticeship Programs. On the basis of these connections, the District Court found that CCC had violated Title VII and section 1981. Tr.C. 32. Before discussing the merits of this portion of the appeal, we must first determine whether the District Court properly exercised jurisdiction over the plaintiffs’ claims against CCC. A charge under this section shall be filed within one hundred and eighty days after the alleged unlawful employment practice occurred and the notice of the charge (including the date, place and circumstances of the alleged unlawful employment practice) shall be served upon the person against whom such charge is made within ten days thereafter.... CCC argues that the District Court lacked subject matter jurisdiction over the plaintiffs’ Title VII claims against it because the plaintiffs failed to adduce any evidence that CCC was named as a respondent in the plaintiffs’ charge filed with the EEOC, that CCC ever received notice of any charges against it relating to rodmen, or that the EEOC issued a notice of right to sue naming CCC. Title VII generally requires that, prior to filing suit in district court, a plaintiff must file a timely charge of discrimination with the EEOC. Within ten days of receiving this charge, the agency is required to notify the respondent named in the charge. 31 Thereafter, the EEOC initiates an investigation, and may attempt to bring about a conciliation between the charging party and the respondent. In general, if after 180 days from the time the charge was filed it remains unresolved, or if the agency dismisses the charge, the EEOC is required to issue a notice informing the charging party and the respondent of the charging party’s right to sue in district court. Specifically, section 706(f)(1) of Title VII, 42 U.S.C. § 2000e-5(f)(l), provides that, once administrative remedies are exhausted, a “civil action may be brought against a respondent named in the charge.” The District Court found that “on September 15, 1975, the Lawyers’ Committee for Civil Rights Under Law [“the Lawyers’ Committee”], on behalf of numerous black rodmen, ... filed a timely third party charge of racial discrimination against all defendants. In September 1976, the Lawyers’ Committee received from the EEOC a notice of its right to sue all defendants.” Tr.F. 6. (emphasis added). At trial, John O’Neil, Executive Director of CCC, testified that CCC had in its files a notice that charges of discrimination had been filed with the EEOC against it, but O’Neil did not identify whether this notice referred to the discriminatory practices at issue in this *1434 case. When the plaintiffs attempted to introduce into evidence the document to which O’Neil referred, the District Court sustained an objection based on the fact that the document was not submitted in accordance with the plaintiffs’ schedule of exhibits and that it was irrelevant because it did not explicitly identify the source or nature of the discriminatory conduct with which CCC had been charged. Tr. at 2006-OS. The plaintiffs have not pointed to any record evidence that supports the contention that a charge against CCC was filed with the EEOC. If the record were no more counter-indicative than this, we might be constrained to conclude that the District Court did not clearly err in finding that the plaintiffs had filed with the EEOC a charge against CCC. In fact, however, the contrary inference is compelled by the record considered as a whole. As CCC points out, the notice of right to sue issued to the Lawyers’ Committee by the EEOC did not name CCC as a respondent. The District Court clearly erred in finding that this notice referred to “all defendants.” With no evidence but O’Neil’s ambiguous testimony to indicate that CCC received notice of the Lawyers’ Committee’s charge, and clear evidence that it did not receive notice of the plaintiffs’ right to sue, the District Court could not reasonably conclude that these plaintiffs had filed a charge of discrimination against this defendant; the District Court’s findings lack competent evidentiary support and are clearly erroneous. The plaintiffs argue that even if a charge was not filed and a right to sue letter was not issued, the District Court could properly entertain the case against CCC. They rely primarily on Zipes v. Trans World Airlines, Inc., 455 U.S. 385, 397, 102 S.Ct. 1127, 1134, 71 L.Ed.2d 234 (1982), in which the Supreme Court stated that “the provision for filing charges with the EEOC should not be construed to erect a jurisdictional prerequisite to suit in the district court.” This statement cannot be used, however, to read out of the statute the administrative procedures with which a prospective plaintiff must comply. As we have stated in the past, “[Title VII’s] statutory enforcement scheme ... embodies a clearly defined policy of deferring action in federal court until a charge has been filed with the agency and an opportunity afforded the agency to attempt private settlement.” Macklin, 478 F.2d at 985-86. Zipes suggests nothing to the contrary. There, the question confronting the Court was not whether a plaintiff can simply disregard the administrative procedures facially made a prerequisite to suit under Title VII; to state that question is to answer it. Instead, Zipes raised the much narrower question “whether the statutory time limit for filing charges under Title VII ... is a jurisdictional prerequisite to suit in the District Court.” Zipes, 455 U.S. at 387, 102 S.Ct. at 1129. The Court held that this time limit was, “like a statute of limitations, ... subject to waiver, estoppel, and equitable tolling.” Id. at 393; see Baldwin County Welcome Center v. Brown, 466 U.S. 147, 152 n. 6, 104 S.Ct. 1723, 1726 n. 6, 80 L.Ed.2d 196 (1984) (“We did not in Zipes declare that the [charge filing] requirement need not ever be satisfied; we merely stated that it was subject to waiver and tolling.”); see also Noe v. Ward, 754 F.2d 890, 892 (10th Cir.1985). Even if exhaustion of the administrative procedures of Title VII is not jurisdictional but is subject to omission when equity so requires, this would not be such a case. First, the plaintiffs argue that CCC had notice of the charges through its “representatives” on the governing committees of the Apprenticeship and Training Programs, both of which bodies were named in the charge. There may be circumstances in which an EEOC charge and right to sue notice against one party may provide notice to another related party sufficient to satisfy the plaintiff’s duty to comply with the legislatively mandated administrative prerequisites to suit. See Kaplan v. International Alliance of Theatrical & Stage Employees, 525 F.2d 1354, 1358-59 (9th Cir.1975). Here, while it is true that CCC appointed trustees to these committees on behalf of its member employers, the committees are distinct legal *1435 entities with which CCC has no ongoing relationship. The relationship between CCC and the committees is too attenuated to conclude that notice to the committees is sufficient to impute notice to CCC. 32 Second, the plaintiffs argue that CCC “waived” the administrative prerequisites because it failed to raise the issue before the trial court in accordance with deadlines for dispositive motions to which the parties and the court agreed. This argument is frivolous. There is no conclusion by the District Court that CCC “waived” the statutory prerequisites to suit; instead, the District Court specifically (and erroneously) found that a charge against “all defendants” had been filed with the EEOC and that a notice of the right to sue had been issued against “all defendants.” In this it erred; so far as the record reveals, the plaintiff failed to comply with the administrative prerequisites to filing suit in the District Court. We therefore reverse the District Court’s judgment holding CCC liable for racial discrimination under Title VII. B. Section 1981 Liability The procedural requirements applicable to Title VII claims need not be satisfied before a claim under section 1981 may be entertained by the courts. Macklin, supra, 478 F.2d at 996. We must therefore still consider the merits of the plaintiffs’ section 1981 claim against CCC. The District Court found CCC liable under section 1981 because it negotiated the collective bargaining agreement with Local 201, Tr.F. 140, appointed trustees to the Training and Apprenticeship committees, Tr.F. 141, and knew or should have known of the discriminatory impact of Local 201’s referral system. Tr.F. 142. As we noted above, in General Building Contractors, supra, the Supreme Court has held that an employers association may be liable under section 1981 for the discriminatory acts of a labor organization with which it has negotiated a collective bargaining agreement only if an agency relationship can be established between the union and the association. The plaintiffs attempt to distinguish this case from General Building Contractors on the ground that CCC is directly, not vicariously, liable for acts of discrimination against the plaintiff classes. The collective bargaining agreement between CCC and Local 201, including the referral clause, is racially neutral on its face. Indeed, it provides expressly that “[t]he Union shall select and refer applicants for employment without discrimination by reason of ... race, creed, color or national origin....” Defendant's Exhibit 10. The agreement operated in a discriminatory manner only because of the local’s restrictive membership policies. CCC’s role as a negotiator in the collective bargaining process is therefore indistinguishable from that of the multi-employer agent in General Building Contractors. See id. at 392-93 n. 18. The plaintiffs claim, however, that unlike the bargaining agent in General Building Contractors, CCC knew or should have known of the discriminatory effects of the referral clause, and the District Court so found. CCC’s willingness to agree to a clause that it knew was discriminatory, it is argued, is itself an act of discrimination. Assuming that the referral system operated in such a way as to discrimi *1436 nate against black rodmen, see Tr.F. 109, Tr.C. 21(h), and assuming for the moment that the District Court did not clearly err in finding that CCC knew or should have known that the referral clause had a discriminatory impact, Tr.F. 142, 144, we nonetheless fail to see how these findings support the inference that CCC itself discriminated. It is undisputed that CCC had nothing to do with Local 201’s membership practices. It is also undisputed that CCC does not play a role in determining which rodmen will be referred to particular jobs. Thus, CCC’s involvement in the referral system was limited to negotiating the facially neutral system’s inclusion in the collective bargaining agreement. Even if the collective bargaining agreement were taken to evidence CCC’s knowledge, indeed its approval, of the local’s discriminatory practices — and we do not so read it — that agreement is not self-executing. Whatever knowledge CCC may have had of the discriminatory practices at issue in this case, the plaintiffs cannot escape the fact that it was the local’s actions and policies that discriminated against the plaintiffs. Therefore, the plaintiffs’ section 1981 claims, insofar as they rely on CCC’s role in negotiating the collective bargaining agreement, depend upon the existence of an agency relationship between CCC and the local. The same conclusion holds true with respect to CCC’s involvement in the Apprenticeship and Training Programs. It is undisputed that the apprenticeship and training committees, not CCC, administer these programs. As a result, CCC’s liability again turns on the existence of an agency relationship, here between it and the committees. We therefore reject the plaintiffs’ attempt to remove this case from the reach of the principles set forth in General Building Contractors. In applying these principles, we first address two of the District Court’s findings that, if not clearly erroneous, would distinguish the facts of this case from those of General Building Contractors. First, the court found that CCC knew or should have known that Local 201 was discriminating against experienced black rodmen and that the referral system “had the effect of implementing and perpetuating racial discrimination.” Tr.F. 142. Cf. General Building Contractors, 458 U.S. at 381, 102 S.Ct. at 3145 (noting that district court found plaintiffs failed to prove that employer associations “were actually aware of the union discrimination”). Second, the court found that “CCC controls access to employment on unionized rodman jobs.” Tr.F. 140. We need not consider whether these findings, taken together or viewed separately, are sufficient to establish the agency relationship between CCC and the other defendants required by General Building Contractors. Our review of the record and the District Court’s reasoning reveals that these findings were conceived in error. There is no direct evidence that CCC knew that the local’s membership practices were discriminatory or that the referral system had a discriminatory effect. Instead, the court found it “proper to infer” that CCC had such knowledge on the basis of four factors: (1) the bargaining relationship between CCC and the local; (2) CCC’s attempt to negotiate the referral clause out of the collective bargaining agreement; (3) a letter in CCC’s file suggesting that the referral system operated by another local was discriminatory; and (4) CCC’s “participation” in the Apprenticeship and Training Programs. Tr.F. 142-44. We take these factors up in turn. (1) CCC employs only two persons. Its primary function is to negotiate collective bargaining agreements on behalf of its member employers. The collective bargaining agreements that it has negotiated with the local, as we stated above, are all facially neutral with respect to race, and the latest agreement expressly requires the local to implement the referral system in a racially neutral manner. CCC does not employ rodmen; it does not police the local’s implementation of their agreement; it has received no complaints from rodmen or employers concerning the discriminatory manner in which the local has implemented the agreement. See Tr. at 1981. We simply fail to understand how the mere fact that CCC negotiated collective bargaining *1437 agreements with the local provides a reasonable basis for inferring the CCC knew or should have known that the referral system had the effect of “implementing and perpetuating” racial discrimination practiced by the Union through its membership policies. (2) We similarly disagree that CCC’s attempt to eliminate the referral clause during its negotiation of the agreements is in any way indicative that CCC knew about the local’s discriminatory practices. There is no evidence to suggest that CCC’s attempt to eliminate the referral clause was based on knowledge of its discriminatory effects. Indeed, CCC maintains that it attempted to eliminate the clause because its employer members wished to have greater control over which employees to hire; seen in this light, CCC’s proposal merely reflects employers’ normal dissatisfaction with the exclusivity of the hiring hall arrangement and the concomitantly higher costs of employing journeyman rather than non-union rodmen. We find this conventional explanation for CCG’s bargaining proposal much more plausible than the speculative proposition that CCC was responding to the local’s discriminatory practices. Absent even a scintilla of evidence that the local’s discriminatory practices played a motivating role in CCC’s decision to seek the elimination of the clause, we do not believe that that decision supports the inference that CCC knew that the clause operated in a discriminatory manner. (3) We are also puzzled by the suggestion that a memorandum in CCC’s files relating to a different local’s referral system supports the inference that CCC knew or should have known of Local 201’s discriminatory policies. The memorandum suggested that the referral system of Local Union 5 may have been operated by that local in a manner that violated the “Washington Plan,” an affirmative action plan to which Local 5 was subject. Local 201 was not subject to the plan. Moreover, even if Local 5’s referral system were identical to Local 201’s (and there is no evidence that it was even similar), it would not follow that CCC’s knowledge that Local 5’s referral system failed to comply with an affirmative action plan provided a basis for inferring that Local 201’s referral system failed to comply with statutory anti-discrimination laws. The inherent illogic of such a leap is magnified when one realizes that the Washington Plan did not purport to operate in a racially neutral manner. The memorandum therefore provides no basis whatever for inferring that CCC knew or should have known of the racially discriminatory practices implemented by Local 201. (4) Finally, we consider the District Court’s finding that “CCC's participation in the Training Program and the Apprenticeship Program is sufficient itself to justify the finding that CCC knew or should have known of the racial discrimination.” Tr.F. 142. We first note that CCC’s participation in these programs is extremely limited. It has no authority over the administration of these programs and does not participate in their actual operation. Instead, CCC’s “participation” is limited to its appointment of three trustees for the Apprenticeship Program and to the appointment of the employers’ representatives to the Training Program. Tr. at 1959-60. We cannot agree that this limited relationship with the educational programs makes it reasonable to charge CCC with knowledge of the local’s discrimination against experienced black rodmen, much less perpetuation thereof through the referral system. There is no evidence of an on-going relationship between CCC and the trustees it appointed, nor even that CCC ever communicated with them. Perhaps the District Court assumed that these trustees acted as CCC’s agents. If so, their knowledge of the local’s discriminatory practices might provide some support for the District Court’s finding. See Restatement (Second) of Agency § 272 (“[T]he liability of a principal is affected by the knowledge of an agent concerning a matter as to which he acts within his power to bind the principal or upon which it is his duty to give the principal information.”). An agency relationship between CCC and *1438 the trustees cannot be assumed, however, on the facts of this case. As the Supreme Court held in General Building Contractors, for the trustees of an apprenticeship program to be the agents of an employer, [t]he employer must ... enjoy a right to control activities of [the apprenticeship committee], and there is no record basis for believing that to be the case. Neither is a right of control inferable merely from the power of the associations to appoint half of the [apprenticeship committee’s] trustees. It is entirely possible that the trustees, once appointed, owe a fiduciary duty to the [apprenticeship committee] and the apprentices enrolled in its programs, rather than to the entities that appointed them. General Building Contractors, 458 U.S. at 395, 102 S.Ct. at 3152 (citing NLRB v. Amax Coal Co., 453 U.S. 322, 101 S.Ct. 2789, 69 L.Ed.2d 672 (1981)). Because we can see no basis on which the District Court could infer that CCC-appointed apprenticeship or training committee trustees acted as CCC’s agents, we cannot accept the District Court’s finding that CCC’s “participation” in those committees is sufficient to infer that CCC knew or had reason to know of the local’s discriminatory practices. We next consider the District Court’s finding that CCC “controls access to employment on unionized rodman jobs.” There is a complete dearth of evidence to support this broad and facially implausible finding. It necessarily implies that CCC “controls” the local, for it is the local that is responsible for the day to day administration of the referral system, which is the exclusive means by which rodmen can obtain employment on unionized jobs. Again, General Building Contractors is instructive: In the run of cases, the relationship between an employer and the union that represents its employees simply cannot be accurately characterized as one between principal and agent.... Indeed, such a conception is alien to the fundamental assumptions upon which the federal labor laws are structured. Id. We therefore reject the District Court’s finding as a clear error. Without the support of clearly erroneous findings, the plaintiffs’ claim, and the District Court’s conclusion that CCC violated section 1981, ultimately rest upon facts that are indistinguishable from those in General Building Contractors. So, too, must be the result. Accordingly, we reverse that portion of the District Court’s judgment holding CCC liable for intentional discrimination under section 1981. VIII. Remedies Defendants challenge several aspects of the District Court’s Amended Order granting relief. Defendants urge that in its Order the District Court “failed to fulfill one of its most basic responsibilities — fashioning remedial relief appropriate to its Trial Findings. Instead, the Court foisted upon Local 201 a groundless judicial mandate which will have far-reaching and permanently harmful effects.” Brief of Local 201 at 120. In crafting Title VII relief, a district court must, of course, “tailor its order[s] to fit the nature of the violation it seeks to correct.” Local 28, Sheet Metal Workers Int’l Ass’n v. EEOC, 478 U.S. 421, 106 S.Ct. 3019, 3050, 92 L.Ed.2d 344 (1986) (“Sheet Metal Workers”). Ordinarily, remedial orders may seek only to eliminate the discriminatory practices at issue; 33 they may not lawfully force a union to admit unlimited members *1439 or to admit unqualified workers. See Texas Dep’t of Community Affairs v. Burdine, 450 U.S. 248, 259, 101 S.Ct. 1089, 1096, 67 L.Ed.2d 207 (1981); Furnco Constr. Corp. v. Waters, 438 U.S. 567, 577-78, 98 S.Ct. 2943, 2949-50, 57 L.Ed.2d 957 (1978). A. The Argument that the Amended Order Impermissibly Requires the Union to Admit Unlimited Numbers of Members Defendants challenge three specific aspects of the Amended Order, which we will discuss in a moment. As an initial matter, however, we deal with defendants’ broadside that the Amended Order imper-missibly requires the Union to admit unlimited numbers of members to its roles. We reject this argument. First, it is not at all clear that the impact of the Amended Order on the Union’s membership ranks will be profound, for the class of plaintiffs is not overwhelmingly large. Second, even if the impact of the Order on the size of Union ranks were significant, the Order does no more than remedy the wrongs done to individual workers who were victims of discrimination. Defendants, we are constrained to conclude, have ignored the remedial nature of the Amended Order. In our view, the District Court was more than justified in seeking to remedy the individual wrongs perpetrated against each class member. B. Special Benefits for Four Named Members Part 11(A) of the Amended Order requires the Union immediately to admit, without requiring any examination or educational training, the four named plaintiffs who (as of the time of the Amended Order) were not yet members. In their briefs, defendants urge that this was an abuse of discretion. However, at oral argument, defendants’ counsel conceded that the particularized relief for the four named members is, from a practical standpoint, no longer at issue. This is so because the Union, even if it prevailed on this point, indicates that it would not seek to remove the two plaintiffs who are now Union members; in addition, the two plaintiffs who have failed to join the Union appear by their own conduct no longer to have an interest in securing Union membership under the umbrella of the specific relief fashioned by the trial court. 34 We thus take- counsel at her word and decline to consider further what appears to be a non-issue. C.Permitting Class Members with 3000 Hours of Experience to Take the Journeyman Exam Without Classroom Training Defendants also object to Part 11(B) of the Amended Order, which (in part) requires the Union to allow class members with 3000 hours of experience to take the journeyman exam without undergoing classroom instruction of any sort. Defendants urge that this requirement ignores the Union’s legitimate interest in assuring that only qualified workers become rodmen, and in limiting its membership ranks. In defendants’ view, the District Court “simply ignored the principle that Title VII remedial orders cannot require the placement of those who lack the appropriate qualifications.” Brief of Local 201 at 127. Defendants argue that the breadth of the court’s remedial power is limited by this unalterable command. We agree with defendants’ articulation of the principle, but disagree that it was violated by this aspect of the District Court’s order. As we have previously indicated, the Union may not lawfully impose the sort of educational requirement it has heretofore mandated as an absolute prerequisite for admission, regardless of a rod-man’s experience and ability. As it should, then, the Amended Order seeks to remove the discriminatory barrier posed by the absolute educational prerequisite. The appropriate way to remedy the injury inflicted on *1440 class members — that is, to put them in the position they would have enjoyed absent discrimination — is to allow them to take the exam once they are sufficiently experienced to do so. Therefore, defendants’ only plausible objection is that 3000 hours constitutes too little experience for the exam alone to serve as a sufficient check to screen out the incompetent. Although we are sympathetic with the proposition that there is no way definitively to determine the precise quantum of on-the-job experience that qualifies one to take the exam, this is, in truth, a reason to affirm the District Court’s choice of 3000 hours. It is, of course, elementary that Congress has granted district courts broad discretion to craft Title VII remedies. See 42 U.S.C. § 2000e-5(g) (1982); see also Sheet Metal Workers, 106 S.Ct. at 3034-35; International Bhd. of Teamsters v. United States, 431 U.S. 324, 364-67, 97 S.Ct. 1843, 1869-70, 52 L.Ed.2d 396 (1977); Franks v. Bowman Transp. Co., 424 U.S. 747, 770-71, 96 S.Ct. 1251, 1266-67, 47 L.Ed.2d 444 (1976). Because 3000 hours is, beyond serious dispute, within a reasonable realm, we cannot say that the District Court abused its discretion in embracing that figure. We disagree with defendants’ objection that 3000 hours has no basis as a measure of experience sufficient to qualify one to become a journeyman rodman. Three thousand hours is obviously substantially more than the level of the experienced pool benchmark (2150 hours), and in our view is sufficiently reasonable to serve as an appropriate standard. We are comforted in this conclusion by two facts: first, the 3000-hours figure was negotiated by the parties; and second, defendants have not come forward with an alternative figure. Defendants downplay the significance of the negotiated nature of the Amended Order, and we agree that under the circumstances that factor is not worthy of great weight. But in determining whether the District Court abused its discretion, the fact that defendants had a hand in negotiating the figure is at least pertinent. Moreover, defendants’ failure to offer an alternative as to the amount of experience sufficient to qualify for entrance to the exam makes us most reluctant to conclude that 3000 hours is outside the bounds of the District Court’s discretion. D. Automatic Membership for Class Members With 6000 Hours of Experience Part 11(B) of the Amended Order also requires that class members with at least 6000 hours of experience be exempted from both classroom training and the journeyman exam, and admitted immediately to full Union membership. Defendants object to this requirement as unwarranted by the record because there has been no allegation or finding that the journeyman exam itself was in any way unlawful. We agree. Indeed, it would be hard to imagine such an allegation since the pass rate on the exam (since the end of the Open Period) was virtually 100 percent. We therefore hold that the District Court abused its discretion in ordering the Union to admit forthwith all class members with 6000 hours of experience, and vacate that portion of the Amended Order. IX. The Union’s Levy of a Speoial Assessment on Members to Finance the Present Litigation In 1982, Local 201 determined that it lacked sufficient funds to meet the legal expenses it had incurred in this case. Accordingly, local officials proposed to levy a special assessment against local members. At the September 1982 union meeting, a resolution to that effect was introduced, discussed and when no objections were raised, approved by a vote of 43 to 14. Local 201’s General Executive Board thereafter ratified the resolution, and each member was assessed $182. When several members refused to pay their assessment, the local instituted internal disciplinary proceedings against them. The plaintiffs moved the District Court for a preliminary injunction to restrain the local from pressing charges against any members of the plaintiff classes. *1441 The parties reached a tentative resolution of this dispute, which the District Court approved. Berger v. Iron Workers Reinforced Rodmen, Local 201, No. 75-1743, Stipulation (D.D.C. Dec. 29, 1983). They established an interest-bearing escrow account into which class members were required to deposit, in periodic installments, an amount equal to their assessment. Local 201 agreed to refrain from taking any assessment-related disciplinary action against members of the plaintiff classes, the plaintiffs agreed that such for-ebearance would be without prejudice to the union’s claim of right to make the assessments, and to impose discipline for non-payment, and both sides preserved their right to appeal the “decision of the [District] Court as to any matter relating to this case....” Id. 35 In its Amended Order of April 11, 1986, the District Court ordered all payments deposited into the escrow account returned to the plaintiffs. The court also permanently enjoined the local from taking any disciplinary action against members of the plaintiff classes “for failure to pay any dues, charges, fees (whether previously levied or levied in the future) assessed against members of Local 201 and/or the International in order to pay for Defendants’ legal fees and other costs of defending this action.” Berger v. Iron Workers Reinforced Rodmen, Local 201, No. 75-1743, Amended Order at 12 (D.D.C. Apr. 11, 1986). The provisions of the District Court’s order respecting the escrow account and the special assessment are not accompanied by findings of fact or conclusions of law. Rather than speculate about the reasoning supporting them, we would ordinarily remand the case to the District Court for further findings. In the circumstances of this too-prolonged litigation, however, a remand would be as unfortunate as it is unnecessary. Given the origin .of such findings and conclusions as the court did enter, we are satisfied that the plaintiffs will present us with any possible reasoning upon which the District Court’s order may have been grounded. As we find their arguments unpersuasive, we have no occasion to remand on this issue. The plaintiffs do not argue that the assessment itself was discriminatory in purpose or effect. The court’s order therefore cannot be justified as a remedy for an independent violation of Title VII or of section 1981. We also reject the plaintiffs’ contention that the Amended Order may appropriately be viewed as an award of compensatory or punitive damages under section 1981. 36 The District Court has neither held hearings on damage issues nor entered a final order determining that compensatory and punitive damages are warranted in this case. See id. at 12. The plaintiffs offer two additional justifications for the order. First, they argue that it would be unjust to require the plaintiff classes to pay for the local’s defense of its discriminatory practices. Second, they argue that the special assessment violates, at least in principle, section 101(a)(4) of the Labor-Management Reporting and Disclosure Act, 29 U.S.C. § 411(a)(4), which makes it unlawful for any labor organization to “limit the right of any member thereof to institute an action in any court....” The special assessment, they claim, effectively “chills” members of the plaintiff classes or members of a class of potential future litigants from asserting their statutory rights. By contrast, Local 201 suggests that the assessment is a legitimate financial obligation for which all members of the Local are responsible. We agree. As the Supreme Court noted in NLRB v. Industrial Union of Marine & Shipbuilding Workers *1442 of America (“Marine Workers”), 391 U.S. 418, 424, 88 S.Ct. 1717, 1721, 20 L.Ed.2d 706 (1968), “§ 8(b)(1)(A) [of the Labor-Management Relations Act] assures a union freedom of self regulation where its legitimate internal affairs are concerned.” 37 Thus, in International Union of Operating Engineers, Local 450, 113 L.R.R.M. (BNA) 1031, 1032 (NLRB Div. of Advice, Mar. 31, 1983), the National Labor Relations Board’s Division of Advice concluded: [A] union is privileged under Section 8(b)(1)(A) to levy uniform assessments on its members to raise money for the purpose of meeting expenses reasonably related to the administration of the Union. Moneys that are expended to defend against charges or suits are reasonably related to the administration of the union. Thus, a union can establish and impose on its membership assessments to cover the costs of defending itself before the Board, where such assessments fall uniformly on all members, including those members who filed the Board charges. Accord Hunter v. United Air Lines, 10 Fair Empl.Prac.Cas. (BNA) 787, 789 (N.D.Cal.1975) [available on WESTLAW, 1975 WL 249]. We can discern no basis upon which to distinguish between an assessment imposed by a union to finance its defense against an unfair labor practice charge and one imposed to finance its defense against a suit brought under the civil rights laws. In each case, the defending union is faced with a charge by one or more of its members that the Union has acted in derogation of individual rights guaranteed by federal law. The plaintiffs’ attempt to argue that charges of racial discrimination involve a “public policy issue,” while unfair labor practices charges do not, is insupportable in reason or in law. Cf. Albemarle Paper Co. v. Moody, 422 U.S. 405, 419 & n. 11, 95 S.Ct. 2362, 2372 n. 11, 45 L.Ed.2d 200 (1975) (noting that the remedial provisions of Title VII were modeled on the remedial provisions of the National Labor Relations Act). We are cognizant that in Title VII Congress has invested the district courts with broad equitable powers “to make possible the ‘fashionpng] [of] the most complete relief possible.’ ” Albemarle Paper, 422 U.S. at. 421, 95 S.Ct. at 2373. Those broad powers, however, are not unbounded. Id. at 416, 95 S.Ct. at 2371. (“That the court’s discretion is equitable in nature ... hardly means that it is unfettered by meaningful standards or shielded from thorough appellate review.”) They do not extend so far into a union’s internal affairs as to control the manner in which it meets the costs of defending itself in court, regardless of the nature of the charges levied against it, unless the union’s method of doing so is unlawful in and of itself. Congress placed procedural conditions on a union’s right to exact dues, fees, and assessments from its members. 38 Once a union has complied with those conditions, and in the absence of any allegation of discriminatory purpose or effect, we believe that Title VII provides no power to the federal courts to undo what the union has legitimately done. We also believe that the asserted “chilling effect” on the plaintiffs’ exercise of statutory rights must be placed in its proper perspective. While we recognize that “[a]ny coercion used to discourage, retard, *1443 or defeat [union members’] access [to legal process] is beyond the legitimate interests of a labor organization,” Marine Workers, 391 U.S. at 424, 88 S.Ct. at 1722, the assessment in this case cannot credibly be regarded as a device to impede union members’ access to the courts. The assessment was imposed only because the funds then available to the local, which also were drawn from the pockets of union members (including, presumably, the plaintiffs who had become union members) in the form of dues or other fees, were insufficient to meet the local’s legal expenses. Absent a finding that an assessment was discriminatory in purpose or effect, that it was imposed to engender hostility between members of the local who did not participate in the plaintiff classes and those that did, see International Union of Operating Engineers, Local 450, 113 L.R.R.M. at 1032, or that the assessment was punitive as applied to members of the plaintiff classes, see Pawlak v. Greenawalt, 628 F.2d 826 (3d Cir.1980), cert. denied, 449 U.S. 1083, 101 S.Ct. 869, 66 L.Ed.2d 808 (1981), we fail to see a proper place for concern about a chilling effect. The universality of the assessment distinguishes it from the assessments imposed by unions that were found in other cases to be unlawful. See, e.g., id. at 828 (union member fined for failing to pursue internal union remedies before filing lawsuit); Ross v. Int’l Bhd. of Electrical Workers, 544 F.2d 1022, 1025 (9th Cir.1976) (same). There is no evidence that this uniform, duly authorized assessment was levied for any purpose other than meeting the union’s legitimate interest in paying its litigation expenses. Nor is there any indication that the amount of the assessment was disproportionate in relation to the expenses actually incurred by the local. We therefore reverse the Amended Order insofar as it requires all funds in the escrow account to be returned to the contributing plaintiffs. We also vacate that portion of the order prohibiting the local from disciplining union members who refuse to pay the assessment. Finally, we direct the District Court to award all funds in the escrow account to Local 201. X. Conclusion Our review of this case has uncovered several clear errors in the District Court’s findings of fact. (1) In particular, we have found that the record does not support the District Court’s findings that the defendants engaged in unlawful retaliation against plaintiffs Berger, Lewis, Jackson, and Kirkland. (2) Nor can we discern any factual basis for the District Court’s finding that the International retaliated against plaintiff Bellamy. We have also concluded that the District Court erred, as a matter of law, in several respects. (1) It was error to allow the plaintiff classes to challenge the high school diploma requirement of the Apprenticeship Program without a suitable class representative. (2) The District Court also erred in holding defendant CCC liable under Title VII and section 1981 for the discriminatory practices of Local 201. (3) Nor can the District Court’s order enjoining Local 201 from disciplining members who fail to pay a duly authorized assessment and requiring Local 201 to return those assessments to the plaintiffs be squared with settled legal principles. Finally, we have concluded that the District Court abused its discretion in ordering Local 201 to admit into membership those plaintiffs having at least 6000 hours of rodman experience without first requiring those plaintiffs to pass the journeyman examination. On the other hand, we have found that the record and settled legal principles support the conclusion that Local 201 and the International, by adopting and implementing the requirement that applicants for union membership complete a Union-supervised educational program, discriminated against the properly certified classes of black plaintiffs in violation of Title VII and section 1981. There is also a sufficient factual basis in the record to support the District Court’s finding that Local 201 engaged in unlawful retaliation against plaintiff Bellamy. Finally, we affirm the District Court’s remedial order, with the exception noted above, as well within the *1444 court’s discretion under Title VII and section 1981. Accordingly, the judgment of the District Court is Affirmed in part and reversed in part. Footnotes [1] The Apprenticeship Program’s high school diploma requirement has since been eliminated. Brief of Appellants Local 201, Apprenticeship Committee and Training Program (“Brief of Local 201") at 40 n. 37. [2] All white rodmen who took the normal entrance exam during this lengthy period passed it, whereas 97.6% of black rodmen (including five workers who took the exam twice) received passing scores. Brief of Local 201 at 19. Dur *1406 ing the Open Period, however, when a different exam was given to non-apprentices, 70.6% (24 of 34) of the white examinees and only 35.3% (12 of 34) of the black examinees passed this special exam. Trial Finding ("Tr.F.”) 76. The appellants do not challenge the accuracy of this finding. [3] CCC contends that the Supreme Court created an exception to the "clearly erroneous" standard in Anderson and mandated de novo review by an appellate court whenever a trial court has "uncritically accepted findings prepared without judicial guidance by the prevailing party.” Anderson, 470 U.S. at 572, 105 S.Ct. at 1511; see Brief of Appellant CCC at 28-30, 40-41. We reject this reading of Anderson. In that case, after noting that its earlier decisions had without exception upheld the "clearly erroneous" standard even when a trial judge had accepted proposed findings verbatim, the Court found that the district court had not “uncritically accepted” proposed findings, and thus that there was "no reason to subject those findings to a more stringent appellate review than is called for by the applicable rules.” 470 U.S. at 572-73, 105 S.Ct. at 1511. We recognize that this language is enigmatic, but we do not believe that it *1408 admits an exception to the standard of review enunciated in Rule 52(a). The Supreme Court nowhere in Anderson so much as mentions the possibility of de novo review by an appellate court, nor does it hold that the standard of review under Rule 52(a) fluctuates with the quality of a district court’s efforts at factfinding. We therefore see no reason to depart from our precedents in this regard. If the record below does not permit a confident assessment of the trial court’s findings, the proper course for an appellate court is to remand for further fact-finding, not to engage in its own guesswork. See Andre v. Bendix Corp., 774 F.2d 786 (7th Cir.1985). We are fortunate indeed that the record in this case allows us to dispose of all the issues raised on appeal without the necessity of a remand. [4] The years in which these six plaintiffs turned 31 are as follows: Berger (1967); Tucker (1968); Jackson (1970); Kirkland (1970); Bellamy (1972); and Lewis (1973). The District Court's finding regarding Bellamy’s age, see Tr.F. 17, was clearly erroneous. Plaintiffs’ counsel acknowledged in oral argument before this court that Bellamy was born on September 18, 1941; his thirty-first birthday therefore fell on September 18, 1972. [5] If we viewed the Apprenticeship Program’s high school diploma requirement as part of a pervasive "pattern of discrimination,” see McKenzie v. Sawyer, 684 F.2d 62, 73 (D.C.Cir.1982), then the plaintiffs might have been able to challenge it even though they alleged injury by the requirement outside of the limitations period, since the requirement, by hypothesis, would have been part of a connected series of violations that extended into the limitations period and at least one element of which was properly contested within that period. However, we reject the suggestion that such a pattern existed in this case, see Part IV.E infra, and reverse the District Court’s contrary finding, Tr. F. 82, as clearly erroneous. [6] For a thorough explanation of the use and role of statistical evidence in Title VII cases, including the nuances of one-tailed or two-tailed tests, see Palmer v. Shultz, 815 F.2d 84 (D.C.Cir.1987). [7] The standards and order of proof in section 1981 cases have been held to be identical to those governing Title VII disparate treatment cases. See Carter v. Duncan-Huggins, Inc., 727 F.2d 1225 (D.C.Cir.1984); see also Stallworth v. Shuler, 777 F.2d 1431, 1433 (11th Cir.1985). As in Title VII disparate treatment cases, section 1981 prohibits only intentional discrimination. See General Building Contractors Ass'n v. Pennsylvania, 458 U.S. 375, 102 S.Ct. 3141, 73 L.Ed. 2d 835 (1982). To make out a claim under section 1981 a plaintiff must demonstrate that he was (1) treated differently than others who were similarly situated (2) because of his race. [8] If defendants identify a racially neutral employment practice in attempting to explain the disparities, a disparate impact analysis is implicated. This is so because defendants will have identified a racially neutral business practice as the cause for racial disparities; under traditional disparate impact analysis, they must also justify the racially neutral employment practice as demanded by business necessity. See Albemarle Paper Co. v. Moody, 422 U.S. 405, 425, 95 S.Ct. 2362, 2375, 45 L.Ed.2d 280 (1975); see also Se- *1414 gar v. Smith, 738 F.2d at 1270; id. at 1303-04 (Edwards, J., concurring). [9] Full Union members are sometimes referred to as "journeymen” or "journeymen rodmen,” and the exam as the “journeyman exam.” [10] No proper challenge to the high school diploma requirement was made; as a result, we have no occasion to consider either statistical model by which plaintiffs sought to prove that the high school diploma requirement disproportionately excluded blacks from the Apprenticeship Program. [11] The parties have assumed, and we do not question their assumption, that Local 201, the Apprenticeship Committee, and the Training Program, although all separately named defendants, are jointly liable for any discriminatory conduct in the operation of the Apprenticeship and Training Programs. [12] Even had the Union kept application records, they would have been of little value for purposes of the statistical analysis in this case, because the fact remains that the Union’s educational prerequisite would have deterred experienced rodmen from applying to take the exam. [13] All permit workers who actually took the exam and became members of the Union were likewise included in the pool of likely examinees, regardless of the number of hours they had in fact worked. [14] The task of identifying "actual examinees” was not difficult because the Union kept records of who took the exam. [15] We note that the percentage of blacks who took the exam was 16.9 percent (21 out of 124). See Tr. F. 80. The minor difference between the percentage of those who took the exam and those who actually became members is attributable to the fact that two blacks failed the exam, and therefore did not become members. Despite this slight discrepancy, we agree that taking the exam can, for all practical purposes, be considered tantamount to becoming a Union member. Over the October 1972-October 1975 period, the pass rate on the journeyman exam for whites was 100 percent, and 97.6 percent for blacks, a difference that plaintiffs concede is not statistically significant. See Brief of Appellees at 69; see also Brief of Local 201 at 19. [16] The District Court stated that the statistical divergence amounted to 3.3 standard deviations. See Tr. F. 82. We have doubts about the District Court’s (or, more accurately, the plaintiffs’) arithmetic accuracy. For the June 1, 1971-October 21, 1972 period, the measures of black and white new members as a percentage of "likely examinees” were 9.2 percent and 33.3 percent respectively, corresponding to 3.25 standard deviations, see Tr. F. 82; for the October 1972-October 1975 period, the respective percentages were 15.3 percent and 33.6 percent — a smaller disparity — yet the District Court found that this corresponded to 3.3 standard deviations. Id. It seems that either (or both) the 3.25 or 3.3 figure is incorrect. Although we doubt the accuracy of some of plaintiffs’ specific statistics, we nonetheless do not doubt that the standard deviations were all above the requisite level of two. More fundamentally, defendants have not challenged these calculations, nor have they disagreed that if we accept plaintiffs’ methodology, the figures show large disparities between the levels of whites and blacks achieving Union membership. We thus see no need to remand this already overlong case for clarification of the District Court’s calculations. [17] Of course, there may be instances in which the relevance of a claimed inadequacy is so obvious that pointing out its omission is sufficient by itself to rebut plaintiffs’ statistical case. See Bazemore, 106 S.Ct. at 3009 n. 10; Palmer v. Shultz, 815 F.2d at 101. [18] The average number of hours for the white examinees during the Open Period was 2150, the benchmark chosen. For blacks, the average was over 2800 hours. See Tr. F. 69. [19] It is appropriate to observe at this juncture that the Training Program, as a Department of Labor-funded affirmative action program, was overwhelmingly comprised of minorities. It is thus hardly surprising that dropouts from the minority-dominated program were predominantly minorities. There were many more experienced non-members over age 30 than under that age; those individuals were overwhelmingly black. Combined dropouts from (as well as combined admissions to) both the Apprenticeship and Training programs would therefore tend to be dominated by the larger Training Program, and thus by minority workers. Moreover, apprentices had more incentive to stay in their program because during the early 1970s, unlike trainees, they paid an initiation fee and full Union dues. [20] Defendants point, plausibly, to two considerations that may reasonably have affected a prospective member's interest in entering the Union's ranks: (1) the mid-1970s represented a time of full employment for rodmen by virtue of the construction explosion occasioned by work on Washington’s subway system; and (2) the abundance of available work created disincentives for Union membership, which was of marginal, if any, immediate utility during a time of full employment. They have not, however, pointed to any reasons why these considerations would operate more strongly on black workers than white. [21] We do not quarrel with the Union's point that blacks over 30 had greater access to Union membership than whites of the same age. This too is irrelevant, though we observe that much of the reason for this state of affairs is that far more non-members over age 30 were black. [22] In this regard, we are frankly troubled by the District Court’s casual intimations to the contrary in view of the record. See Tr.F. 14, 103-OS. The weight of the evidence, which the District Court chose not to treat specifically, clearly was that the Training Program classes were substantive. See, e.g., Tr. 1514-15 (volume h) (Testimony of Mr. Grigsby, Local 201’s Business Manager); Tr. 1830-43 (vol. k) (Testimony of Mr. Masler, an instructor in the Training Program). Unfortunately, the trial court failed to address the evidence, and we are left without the benefit of the District Court’s specific views in this respect. [23] This time-frame theoretically includes some workers who were experienced (and therefore delayed membership by virtue of the Apprenticeship Program) prior to the institution of the Training Program in September 1972. It certainly includes workers who were experienced, yet were deterred by the barrier of Apprenticeship or Training after September 1972. [24] Lewis testified: Q: So [Gilmer] didn’t tell you that you had to drop [the charges] in order to get in the program. A: No, he asked me was I willing to drop the charges. Tr. at 469. [25] We do note that Berger testified that after Gilmer stated that he "was going to make it hard” on the plaintiffs, Berger worked only a total of four days in the sixteen-month period preceding trial. Berger’s testimony was rebutted by pension records indicating that he worked over 1200 hours in this period, more than the average journeyman. We must assume that the District Court credited the rebuttal evidence since there is no finding that Berger suffered from retaliation in being denied referrals. [26] See McDonnell Douglas Corp. v. Green, 411 U.S. 792, 799-800, 93 S.Ct. 1817, 1822-23, 36 L.Ed.2d 668 (1973) (emphasis added): [27] Even if the argument pressed by the plaintiffs were properly before this court, Goodman would not be controlling. There is no evidence that Kirkland appealed to the defendants for relief through grievance or other available procedures. In Goodman, the Court specifically declined to address the question whether "mere passivity" in the face of employer discrimination against union members is sufficient to establish a claim under Title VII or section 1981 against the union representing those employees. Goodman, 107 S.Ct. at 2623. Even “mere passivity,” however, implies that the defendants were at least aware of the employer’s discriminatory practice. Although we may assume that Local 201 was aware of Kirkland’s layoff, we cannot first assume, in the absence of any evidence, that any of the defendants knew, should have known, suspected, or should have suspected that the layoff was made for other than legitimate business reasons. [28] Although the plaintiffs appear to argue that the layoff itself was retaliatory, see Brief for Appellees at 83, this claim is not supported by the District Court's findings; we therefore decline to address this issue. [29] The traditional indicia of an agency relationship include “(1) consent; (2) fiduciary duty; (3) absence of gain or risk to the agent; and (4) control by the principal.” Boss, 567 F.Supp. at 847 n. 1 (quoting H. Reuschlein & W. Gregory, Agency and Partnership 11 (1979)). [30] Where a union’s failure to act violates Title VII or section 1981, the discriminatory practices of the organization that the union failed to oppose may nonetheless weigh heavily in fashioning appropriate relief. If those discriminatory practices would not have occurred but for the union’s failure to act, the union may be required to redress the injuries sustained as a result of those practices. It may remain open to the union, however, to demonstrate that even if it had acted, and satisfied its affirmative duty, the other organization’s practices would not have been altered and the injuries would not have been prevented or abated. We express no opinion on whether such a showing would be sufficient to relieve a union of responsibility for remedying such injuries. [31] 42 U.S.C. § 2000e-5(e) provides, in relevant part: [32] In Gray v. International Bhd. of Electrical Workers, 10 Fair Empl.Cas. (BNA) 565 (D.D.C.1975), the District Court allowed plaintiffs to maintain a Title VII action against an employers association not named in the administrative charge. The court found that the association received "ample notice" of the EEOC charges because it was a member of a "related” joint apprenticeship and training program that received notice of the administrative charge. Even if we were to regard this authority as persuasive, however, this case is quite different. CCC is not a "member” of either the Training or the Apprenticeship committee, nor is there any indication that CCC is otherwise "related" to the committees. We further note that there is no allegation here that CCC is an indispensable party under Federal Rule of Civil Procedure 19, which in some circumstances may provide a basis for joinder of a party in a Title VII suit despite the absence of any charge filed with the EEOC naming that party as a respondent. See Evans v. Sheraton Park Hotel, 503 F.2d 177 (D.C.Cir.1974). [33] In some situations, where past discrimination has been persistent and obstinate, relief going beyond traditional make-whole remedies has been deemed appropriate. See, e.g., Sheet Metal Workers, 106 S.Ct. at 3035-37; United States v. Paradise, — U.S. -, 107 S.Ct. 1053, 94 L.Ed.2d 203 (1987). This is obviously not such a case, see supra, Part IV.E. Moreover, the relief ordered in this case is not the sort of a race-conscious affirmative relief challenged in cases such as Sheet Metal Workers and Paradise. In this case, the Amended Order grants relief only to specific victims of discrimination, namely the members of the plaintiff classes; the relief here is entirely backward looking, imposing on defendants no future burdens to achieve any sort of specific racial percentages. In short, this case deals only with traditional make-whole relief. [34] The Amended Order, which was entered on April 11, 1986, has been in effect for more than a year. See Brief of Appellees at 3. According to counsel’s representations at oral argument, two of the specially benefited named plaintiffs are today members of Local 201, and two have chosen, for whatever reason, not to take advantage of Part 11(A) of the Amended Order. [35] We reject as frivolous the plaintiffs’ suggestion that, having submitted this issue to the District Court, the defendants are somehow foreclosed from arguing that that court exceeded its remedial powers in ordering the escrowed funds returned to the plaintiffs. [36] See Harris v. Richards Manufacturing Co., 675 F.2d 811, 814 (6th Cir.1982): "a private plaintiff who sues under both Title VII and Section 1981 may obtain the equitable relief provided by Title VII and such equitable relief as well as legal relief by way of compensatory and punitive damages afforded by Section 1981.” [37] Section 8(b)(1)(A) forbids labor organizations from restraining or coercing employees in the exercise of guaranteed rights, but makes an exception for the union’s "right ... to prescribe its own rules with respect to the acquisition or retention of membership....” 29 U.S.C. § 158(b)(1)(A). [38] Section 101(a)(3)(A) of the Labor-Management Reporting and Disclosure Act of 1959, 73 Stat. 519, 522, 29 U.S.C. § 411(a)(3)(A), requires that no general or special assessment shall be levied upon [members of a local union], except ... (i) by majority vote by secret ballot of the members in good standing voting at a general or special membership meeting, after reasonable notice of the intention to vote upon such a question, or (ii) by a majority vote of the members in good standing voting in a membership referendum conducted by a secret ballot.... The plaintiffs do not dispute that the provisions of the LMRDA have been fully complied with.