ROBERT MADDEN HILL, Circuit Judge:
Fourteen black policé officers sued the city of Vicksburg, Mississippi, and its officials for allegedly discriminatory employment practices. Vicksburg used a standardized test to assess qualification for promotion, and this test disproportionately impaired the promotional opportunities of blacks on the police force. Because the district court improperly placed the burden upon the plaintiffs to show the job-relatedness of the test, we reverse and remand. We vacate the award of attorney’s fees in [387]*387light of the plaintiffs’ greater success. In all other respects, we affirm.
I. PROCEDURAL HISTORY AND BACKGROUND
In 1976 eight black policemen, including Roosevelt Bunch and John Minor, filed suit against the mayor, chief of police, chairman and members of the civil service commission, and personnel director of the city of Vicksburg, Mississippi. Originally filed as a class action, alleging claims of racial discrimination in employment based on 42 U.S.C. §§ 1981 and 1983,1 class certification was later denied for lack of numerosity. The complaint was amended in 1977, adding two more black policemen as plaintiffs, including Willie James (“Bill”) Williams, and naming the Mayor and Aldermen of the City of Vicksburg (“Vicksburg”) as another defendant, as well as adding Title VII claims under 42 U.S.C. § 2000e et seq. Four more plaintiffs were added in a 1978 amendment.
After a bench trial, the district court granted relief to Bunch and Minor by directing Vicksburg to promote them to lieutenant and by awarding them back pay starting from two years prior to the date suit was filed. The court dismissed the claims of the other twelve plaintiffs, and dismissed all claims against individual defendants. Vicksburg was enjoined “to maintain non-discriminatory promotion policies pursuant to the valid Civil Service Regulations presently in existence” at the Vicksburg Police Department. The court also directed that the next opening for captain be filled by a qualified black police officer. Finally, the court awarded the plaintiffs their attorney’s fees but denied Bunch and Minor prejudgment interest on the back pay awards.
Although certain individual instances of alleged discrimination will be addressed in the discussion of legal issues, the following is a general description of the promotion policies at the police department. Bunch and Minor were the first two black policemen in Vicksburg, both hired in 1963. Until 1974 promotions were determined largely subjectively, although a patrolman could automatically receive a promotion to - sergeant by volunteering for motorcycle duty. Sergeants who then served in an administrative capacity could qualify for promotion to lieutenant. These policies created a large number of sergeants and lieutenants in the department, and promotions were temporarily halted in 1974.
In 1976, pursuant to revised civil service rules, Vicksburg began using examinations prepared by a private firm, International Personnel Management Association (IPMA). The district court found that of the twenty-eight policemen who took IPMA exams, fifteen passed, but only three of thirteen black policemen passed. In 1978 Vicksburg stopped giving IPMA tests and the police department and civil service commission developed its own exams. However, several plaintiffs, many acting on advice of counsel, refused to take any of the locally created exams. None of the tests taken by the plaintiffs were introduced into evidence.
The twelve plaintiffs who were denied relief have appealed, and Vicksburg cross-appeals against all plaintiffs. After the district court determined the amount of attorney’s fees, these twelve plaintiffs also appealed that ruling. The two appeals are now consolidated.
II. ISSUES ON APPEAL
A. Title VII Threshold Issues
1. Timeliness
Vicksburg argues in several ways that the district court should not have considered the Title VII claims that were added to the complaint in a May 19, 1977, amendment. First, Vicksburg, argues that this amendment came too late because it [388]*388was added more than ninety days after the dates of the EEOC “right to sue” letters, January 17 and 28, 1977. These letters were the result of EEOC investigations initiated by plaintiff Bill Williams. The statute provides that the EEOC “shall notify the person aggrieved and within ninety days after the giving of such notice a civil action may be brought____” 42 U.S.C. § 2000e-5(f) (emphasis added); see Espinoza v. Missouri Pacific Railroad Co., 754 F.2d 1247, 1250 (5th Cir.1985) (ninety-day period generally begins when notice given at address designated by claimant).
However, while the actual amendment came too late, the plaintiffs had moved to amend (to add Bill Williams and the Title VII claims) on April 18, 1977. Although this motion came ninety-one days after January 17, the court recognized that the relevant date was the date of receipt of the right to sue letter, and took judicial notice of the fact that ordinary mail does not travel from Washington to Mississippi in one day. Thus, the ninety-day clock did not start ticking until January 18, at the earliest, and the April 18 motion was timely. The motion to amend alerted the parties and the district court to the coming Title VII claims, and thus “curative steps” were taken within the ninety-day period. Cf. Stewart v. City of Pontotoc, Miss., 461 F.Supp. 767, 775 (N.D.Miss.1978).
2. Statute of Limitations.
Vicksburg also argues that the district court erred in considering some of the plaintiffs’ claims under Title VII2 which accrued before the applicable statute of limitations would allow. The limitations provision of Title VII requires that “[a] charge under this section shall be filed within one hundred and eighty days after the alleged unlawful employment practice occurred____” 42 U.S.C. § 2000e-5(e). “This limitations period begins to run from the time that the complainant knows or reasonably should know that the challenged act has occurred.” McWilliams v. Escambia County School Board, 658 F.2d 326, 328 (5th Cir.1981). The district court found that Bill Williams had filed an EEOC charge in “early 1975,” but could not determine the exact date from the evidence presented.3
We find Vicksburg’s contention to be without merit. Vicksburg can indicate no alleged unlawful employment practice, relied upon by the district court, which occurred prior to mid-1974. Plaintiffs Bunch and Minor were found to be victims of continuing discrimination, which extended well into the relevant period. The district court denied the disparate treatment claims of the other twelve plaintiffs, rulings which we affirm on the merits; we need not reach a limitations threshold question raised by Vicksburg's cross-appeal. See infra part II F. The IPMA exams were first administered in 1976. No reversible error is shown.
3. Single Filer Rule
Vicksburg contends that the January 1977 right to sue letters concerned the EEOC’s investigation of Bill Williams’ complaints of broad, general discrimination in the police department prior to 1976. Bill Williams was the only plaintiff who filed charges with the EEOC. In general, time[389]*389ly filing of EEOC charges is a prerequisite to a Title VII suit. See Wheeler v. American Home Products, 582 F.2d 891, 897 (5th Cir.1977). According to Vicksburg, the district court cannot inquire into post-1976 discrimination claims such as the IPMA exams. The question is one concerning the “single-filer” rule: whether the claims of the plaintiffs who did not file EEOC complaints are “similar enough” to that of Bill Williams’ so that the purpose of the filing requirement (that settlement first be attempted through the EEOC) not be frustrated. See Ezell v. Mobile Housing Board, 709 F.2d 1376, 1381 (11th Cir.1983).
Although the IPMA tests were new, the same parties were charged with discrimination against blacks in failing to promote them. Moreover, once litigation was underway, the possibility of settlement through the EEOC was remote. There is no indication in the record that the EEOC could have acted on such charges quickly enough to have caused expedition in disposition of the lawsuit. Vicksburg does not indicate why, after suit has been filed, fresh appeal should be had to the EEOC every time the defendants use a new method to discriminate against the same persons. See Crawford v. United States Steel Corp., 660 F.2d 663, 666 (5th Cir.1981) (single filer rule applies when “gravamen of complaints” is the same: all plaintiffs were passed over for promotion because of race). Separate serial filings by all plaintiffs would be a “needless procedural barrier.” Cf. Gupta v. East Texas State University, 654 F.2d 411, 414 (5th Cir.1981) (plaintiff need not file second EEOC charge to sue for alleged retaliation for his first charge).
4. Mootness
Vicksburg argues that all of the Title VII promotion claims became moot when Bill Williams quit the department. Vicksburg contends that as the only plaintiff to file with the EEOC, when Williams lost his own standing he also deprived all the other plaintiffs of standing. See Backus v. Baptist Medical Center, 671 F.2d 1100 (8th Cir.1982). However, there have been no factual findings by the district court to substantiate Vicksburg’s argument that Williams’ claim was moot. Had Williams been intentionally denied promotion oh account of race while still working for the Vicksburg Police Department, he would be entitled to back pay to remedy the differential in compensation caused by the racial discrimination.4 Even though a claim for past due wages may be “tiny” in dollars, “it is enough on which to launch a full scale inquiry into the charged unlawful motivation in employment practices.” Jenkins v. United Gas Corp., 400 F.2d 28, 33 (5th Cir.1968). Moreover, since Williams failed an IPMA examination and was denied a promotion, his claim under disparate impact' analysis is very much alive. See infra part II E. We cannot conclude that Williams’ claim was extinguished by his later acceptance of other employment.
B. Individual Back Pay With General Injunctive Relief.
Plaintiffs complain that the district court acted inconsistently in fashioning general injunctive relief while awarding back, pay to only two of the fourteen plaintiffs. Although class certification was denied, plaintiffs contend that their group was a “sort of class action” requiring class-wide back pay. Cf. Jenkins v. United Gas Corp., 400 F.2d 28, 33 (5th Cir.1968) (class plaintiff’s acceptance of promotion does not moot individual or class-wide claims for injunctive relief). The plaintiffs argue that by ordering the continuation of non-discriminatory employment practices and the promotion of an unspecified black to captain, the district court implicitly found discrimination against all plaintiffs. They ask [390]*390for application of the rule that “[0]nce a court has determined that a plaintiff or complaining class has sustained economic loss from a discriminatory employment practice, back pay should normally be awarded unless special circumstances are present.” See Pettway v. American Cast Iron Pipe Co., 494 F.2d 211, 252-53 (5th Cir.1974); see also Salinas v. Roadway Express, Inc., 735 F.2d 1574, 1578 (5th Cir.1984).
Plaintiffs’ argument fails because the district court found that none of the plaintiffs other than Bunch and Moore proved any economic loss resulting from racial discrimination. While the merits of the individual claims will be discussed below, Pettway does not require that relief be granted an individual non-class member who has suffered no identifiable harm. The district court found that Vicksburg did intentionally discriminate against “several” of the plaintiffs, and that the standardless, pre1976 system of promotion “has generally affected the advancement of blacks on the force, and that this system was maintained until approximately 1976 with the realization that it did so.” However, given the court’s other findings, it is apparent that the court was referring either to Bunch and Moore or to practices occurring before the beginning of the applicable limitations period. The court examined the claims of the other plaintiffs, and found in each case that they received timely promotions or else that there was a legitimate reason for not promoting them. Thus, the court reached the “equities of individual cases.” See Albemarle Paper Co. v. Moody, 422 U.S. 405, 413, 95 S.Ct. 2362, 2369, 45 L.Ed.2d 280, 294 (1975). Even though the injunctive relief benefits parties other than Bunch and Moore, it can still be proper when sought by the individual plaintiff. See Meyer v. Brown & Root Construction Co., 661 F.2d 369, 374 (5th Cir.1981) (injunctive relief otherwise proper, although benefiting non-party, but found unwarranted because not sought by plaintiff).5
C. Bifurcation
Plaintiffs argue that the district court erred in failing to bifurcate the trial on the issues of liability and damages. At the close of the evidence, the court asked counsel for both sides whether there had been a ruling to bifurcate the trial. Plaintiffs’ counsel then explained his assumptions about the normal procedure but did not move to bifurcate:
We understood, Your Honor, from the plaintiff’s viewpoint, that that was the custom of the Court in this district, and that that was the — the practice that this — that Your Honor would follow in these types of matters. I specifically do not recall whether that was specifically stated at the time of the pretrial conference, but I thought the Court indicated that’s how it intended to proceed. That’s why I had not raised the issue previously-
Counsel for Vicksburg stated to the court his recollection that there was no ruling to bifurcate, and proceedings resumed on other matters without an express ruling on the issue. Plaintiffs’ evidence had been confined largely to the issue of liability, but Vicksburg later agreed to stipulate damages for Bunch and Minor. The proper procedure after establishing liability, according to plaintiffs, would have been for the court to reopen the record and resolve the extent of individual losses. Plaintiffs’ contention is without merit.
Generally, issues must be presented to the district court to receive appellate consideration unless to ignore them would result in a “fundamental miscarriage of justice.” See Mitchell v. M.D. Anderson Hospital, 679 F.2d 88, 91-92 (5th Cir.1982). Plaintiffs do not now allege that they ever moved for bifurcation or that the district court so ruled, and the record indicates that plaintiffs’ counsel merely assumed the trial would be in two stages. There is no indica[391]*391tion that plaintiffs ever attempted to introduce evidence on the amount of back pay. Moreover, the sole case relied upon by plaintiffs in contending for a right to bifurcation, Baxter v. Savannah Sugar Refining Corp., 495 F.2d 437, 443-44 (5th Cir.), cert. denied, 419 U.S. 1033, 95 S.Ct. 515, 42 L.Ed.2d 308 (1974), which stated that “[a] Title VII class action suit presents a bifurcated burden of proof problem,” does not support reversal on this ground. Baxter held only that the district court had acted prematurely in requiring individual proof of economic loss in its denial of class-wide back pay. Here, however, class certification was denied and no presumption of class-wide back pay was brought into operation. In addition, plaintiffs suffered no prejudice, for the parties later stipulated to the amounts of back pay due to Bunch and Minor, the only two individuals found by the district court to have been discriminated against.6 We perceive no miscarriage of justice.
D. Exclusion of Deposition
Plaintiffs argue that the district court erred in barring their use of the deposition of Otis Williams, a defendant and a member of the civil service commission, during his testimony at trial. Plaintiffs had called Williams in the middle of the week-long trial as an adverse witness and attempted to use his deposition to contradict his trial testimony that the promotion system was uniform. Defendants objected because the deposition was not filed with the District Clerk or signed. See Fed.R.Civ.P. 30(e), (f). This deposition, although taken two years prior to trial, was not transcribed until the week before trial, and the defendants did not receive a copy until the morning of Williams’ testimony. Plaintiffs claim that any errors in the handling of the deposition were waived, citing Fed.R.Civ.P. 32(d)(4), which provides that “[ejrrors and irregularities in the manner in which the testimony is transcribed or the deposition is prepared, signed, certified, sealed, indorsed, transmitted, filed, or otherwise dealt with by the officer under Rules 30 and 31 are waived unless a motion to suppress the deposition or some part thereof is made with reasonable promptness after such defect is, or with due diligence might have been, ascertained.”
The local rules of court did not ordinarily require the filing of a deposition. See S.D. Miss.R. 22(1) (version in effect at time of trial); see also Fed.R.Civ.P. 5(d). However, the local rules did require that a copy of the deposition coversheet be filed “forthwith” after receipt of the transcript, and that the deposition itself be filed at the outset of trial if reasonably anticipated that it would be used at trial. S.D.Miss.R. 22(1), (2) (version in effect at time of trial). The Federal Rules call for depositions to be signed either by the witness, or, under some circumstances, by the officer before whom the deposition was taken. See Fed. R.Civ.P. 30(e). The waiver provisions of Rule 32(d)(4) contemplate that objections to violations of technical requirements be unavailable at trial absent a prompt motion to suppress. See 4A J. Moore, J. Lucas & D. Epstein, Moore’s Federal Practice § 32.11 (2d ed. 1984). Nevertheless, here the defendants were denied such an opportunity to suppress by the plaintiffs’ last minute presentation of the deposition. The district court recognized that the defendants’ objection was not a technical one, for it was based on their complete unawareness that the deposition was to be used at trial or that it had even been transcribed. The defects in the deposition in regard to the filing and signing requirements were thus not ascertainable. Cf. McVay v. Cincinnati Union Terminal Co., 416 F.2d 853, 856 (6th Cir.1969) (“[T]he failure promptly to file is harmless where the adverse party saw the deposition prior to trial.”). We find no error in the district court’s reconcil[392]*392iation of the Federal Rules and the local rules.
E. Disparate Impact — Promotional Exams
The disparate treatment and disparate impact theories of employment discrimination differ in their approach to. the factual issues of Title VII claims. Under a disparate treatment theory, the plaintiff must show that the defendant intentionally discriminated against him. See U.S. Postal Service Board of Governors v. Aikens, 460 U.S. 711, 715, 103 S.Ct. 1478, 1482, 75 L.Ed.2d 403, 410 (1983). Proof of discriminatory intent may be made by direct or circumstantial evidence. Id. at 714 n. 3, 103 S.Ct. at 1481 n. 3, 75 L.Ed.2d at 409 n. 3. The framework for proof of a disparate treatment claim may involve a three-step process of the plaintiff proving a prima facie case, the defendant articulating a legitimate reason for the employment decision, and finally the plaintiff proving this reason a mere pretext. E.g. Texas Department of Community Affairs v. Burdine, 450 U.S. 248, 252-53, 101 S.Ct. 1089, 1093, 67 L.Ed.2d 207, 215 (1981). See also infra part II F.
Under a disparate impact theory, on the other hand, the employer’s intent to discriminate is not at issue. Pouncy v. Prudential Insurance Co. of America, 668 F. 2d 795, 800 (5th Cir.1982). “In order to establish a claim of racial discrimination under this theory, a plaintiff need only show that a facially neutral employment practice produces a significantly adverse impact on one race.” Id. (citation omitted). “A prima facie case [of disparate impact] is shown by identification of a neutral employment practice coupled with proof of its discriminatory impact on the employee’s work force.” Id. (citation omitted). See also Dothard v. Rawlinson, 433 U.S. 321, 329, 97 S.Ct. 2720, 2726-27, 53 L.Ed.2d 786, 797 (1977). A typical target of disparate impact analysis is an aptitude test used to screen applicants for promotion or hire. See Pouncy, 668 F.2d at 801.
The district court, through a process which was without doubt careful and diligent,7 found that the IPMA tests had a significantly disproportionate impact on black police officers:
The testing procedures which were employed by the police department were not put into place until 1976. Even after their use it was obvious to the officials in the Police Department that they had an impermissible impact on black officers seeking promotion by way of tests. The statistics show that few black officers passed examinations and many white officers passed them. During the period between September of 1976 and December of 1977 the black officers participated in the testing program with apparent vigor. Unfortunately, because of the nature of the tests there was again little opportunity for advancement for black officers because of the impact which these tests had on black officers.
* * * # # *
It is possible that some of the Plaintiffs have the subjective qualifications for promotion but they have failed to take the requisite promotional exams or did not pass them____ The exams given before 1978 have been viewed suspiciously by this Court because of the statistically adverse impact on the black officers taking the exams.
The question of the existence of discriminatory impact is a factual one for the district court, to be disturbed on appeal only if found to be clearly erroneous. Walls v. Mississippi State Department of Public Welfare, 730 F.2d 306, 319 (5th Cir.1984). The content of the clearly erroneous rule is well established: “A finding is ‘clearly erroneous’ when although there is evidence [393]*393to support it, the reviewing court on the entire evidence is left with the definite and firm conviction that a mistake has been committed.” United States v. United States Gypsum Co., 333 U.S. 364, 395, 68 S.Ct. 525, 542, 92 L.Ed. 746, 766 (1948); see also Anderson v. Bessemer City, 470 U.S. 564, 105 S.Ct. 1504, 84 L.Ed.2d 518 (1985).
Plaintiffs argue that the district court, after recognizing the adverse impact the IPMA exams had on blacks seeking promotion, erred in placing onto plaintiffs the burden of showing that the exams were not legitimately job related. Plaintiffs argue that once an employment test is shown to be discriminatory in effect, the burden of showing its relationship to the employment in question is properly placed on the employer. The district court blamed the plaintiffs for not producing the exams at trial, and concluded that “There is no proof that these exams were not sufficiently job related to pass muster under Title VII.” The district court applied the following legal standard when evaluating the effect of the absence of the IPMA exams (emphasis supplied):
This Court may have reached a different conclusion if the actual tests given were before it for analysis; however, this apparently important aspect of this litigation has not been brought before the Court by the Plaintiffs, it being their burden to do so, and there is no indication of the Defendants’ bad faith in the destruction of the exams and their failure to present the Court with this information.
Plaintiffs contend that any inferences drawn from the absence of the exams should be in their favor, since they made a general discovery request8 and Vicksburg has destroyed9 all exams taken in 1976-77.
The district court erred by reversing the proper burden of proof on this issue and thus applying a standard contrary to settled law. “Title VII forbids the use of employment tests that are discriminatory in effect unless the employer meets ‘the burden of showing that any given relationship [has] ... a manifest relationship to the employment in question.’ ” Albemarle, 422 U.S. at 425, 95 S.Ct. at 2375, 45 L.Ed.2d at 300-01 (emphasis added) (quoting Griggs v. Duke Power Co., 401 U.S. 424, 432, 91 S.Ct. 849, 854, 28 L.Ed.2d 158, 165 (1971)). After an employer meets the burden of proving its tests to be job related, the plaintiff may then show the tests to be a mere pretext for discrimination. Id; see Dothard v. Rawlinson, 433 U.S. 321, 329, 97 S.Ct. 2720, 2727, 53 L.Ed.2d 786, 797 (1977); Page v. U.S. Industries, Inc., 726 F.2d 1038, 1053 (5th Cir.1984), However, Vicksburg never introduced any evidence of the job relatedness of the IPMA exams, although it had the burden of doing so. Vicksburg has failed to allege or prove any relationship between the aptitudes tested for by the IPMA exams and the functions of a Vicksburg police officer.10 The dis[394]*394trict court improperly inferred from this absence of evidence that these unvalidated exams were a permissible means of refusing to promote certain plaintiffs. Vicksburg effectively concedes that the district court misstated the law.
Vicksburg makes two arguments in an attempt to excuse the district court’s error. First, Vicksburg contends that the plaintiffs were “lying behind a log” by waiting until after trial to press their claims of disparate impact. Vicksburg thus suggests that the plaintiffs have waived their disparate impact claims. Second, Vicksburg argues that there was no proof that the exams had an adverse impact on blacks to justify use of a disparate impact theory. According to Vicksburg, the statistics culled by the district court during trial were too few and incomplete to form a causal relationship between the exams and discriminatory effects on the black policemen.
We disagree with each of Vicksburg’s proffered justifications for the district court’s error. The plaintiffs have maintained throughout the ten-year history of this litigation that the exams were discriminatory. First, plaintiffs’ suit was filed soon after the IPMA exams were instituted. One of the allegations of the complaint was that Vicksburg failed to promote black applicants. In a pretrial factual summary served upon Vicksburg, the plaintiffs alleged that one form of racial discrimination was the standardized tests given to all applicants for promotion. Vicksburg’s response to this factual summary argued that these “uniform standards and testing procedures” were not discriminatory, and then proceeded to justify the non-promotion of certain blacks by pointing to their prior poor performance on the tests. In a pretrial order, the plaintiffs alleged that they were denied promotion and “subjected to a discriminatory testing program,” and Vicksburg again responded by acknowledging the poor performance of several blacks in test-taking. As early as 1978, six years before trial, the mayor of Vicksburg received a letter from the Federal Office of Revenue Sharing explaining the results of an investigation into allegedly discriminatory employment practices in Vicksburg city government. The letter, introduced into evidence at trial, stated that “the Personnel Director admits, and the evidence thus discloses, that the police entry and promotional examinations have a disparate impact on blacks as a class.” 11 It is difficult to imagine how Vicksburg could defend an objectively answered, facially neutral testing procedure without realizing that its concededly discriminatory impact could be subject to challenge.
Moreover, the use of the IPMA examinations was an employment practice well-suited for disparate impact analysis. “The use of a test is a specific, facially neutral selection criterion that can be shown to have a causal connection to a racial imbalance in the work force. This selection criterion is the kind of employment practice to which the disparate impact model traditionally has applied.” Carroll v. Sears, Roebuck & Co., 708 F.2d 183, 189 (5th Cir.1983). While we know little about the content of the IPMA examinations, it is clear that they were a “specific facially neutral selection criterion.” Id. In contrast, an allegedly discretionary promotion procedure fits within the disparate treatment analysis, rather than the disparate impact analysis. Lewis v. NLRB, 750 F.2d 1266, 1271 (5th Cir.1985). Pre-1974 promotions were largely subjective, as the district court recognized, but Vicksburg’s pleadings and evidence adduced at trial indicated that poor performance on a later IPMA examination [395]*395often ruined an applicant's opportunities for promotion. Cf. Carroll, 708 F.2d at 188-89 & n. 3 (test which neither qualified nor disqualified an applicant from being hired or promoted does not fit disparate impact model). Without the aid of disparate impact theory, a plaintiff faces an almost insuperable handicap in challenging a facially neutral employment requirement. Forcing such a job criterion into the Procrustean bed of disparate treatment analysis was error.
Second, we find that the plaintiffs presented evidence sufficient to uphold the determination of the district court that the IPMA exams had a disparate impact on black applicants for promotion. According to the unchallenged findings of the district court, twelve of fifteen (or 80%) of white applicants for promotion passed the IPMA exams, while only three of thirteen (or 23%) of blacks passed. The threshold inquiry, and the trigger of the employers’ burden to prove job relatedness, is whether the plaintiffs have shown that “the tests in question select applicants for hire or promotion in a racial pattern significantly different from the pool of applicants.” Albermarle, 422 U.S. at 425, 95 S.Ct. at 2375, 45 L.Ed.2d at 280. The tests must be “significantly discriminatory” or at least create percentages which are “markedly disproportionate.” See Rivera v. City of Wichita Falls, 665 F.2d 531, 534-35 (5th Cir.1982). Although the sample size is small,12 we believe that the observed disparity is great enough to permit the conclusion that a prima facie case of disparate impact has been established. See id. at 536 n. 7. “[T]he limited size of the population in question [does not preclude us] from recognizing a decisive pattern emerging from a history of experiences.” Id. “A plaintiff may use statistical as well as non-statistical evidence in establishing a prima facie case of disparate impact.” Page, 726 F.2d at 1053. The same pattern of racial selection, if imposed on a larger work force, would without question provide statistically significant results. While often helpful, standard deviation techniques are not the sole measure of the impact of a facially neutral requirement. We cannot permit an employer to escape liability for discriminatory tactics merely because his work force is not vast enough to provide meaningful data for a sophisticated statistical evaluation.
We remand to the district court to allow it full opportunity to award relief under a disparate impact analysis. Plaintiffs have already established a prima facie case of general discriminatory effect, and Vicksburg has utterly failed to show the job relatedness of the IPMA exams. These issues are not open for redetermination on remand. We leave it to the district court in the first instance to identify the plaintiffs who have been denied or delayed in their efforts to achieve promotion as a result of the IPMA exams. The district court thereupon shall fashion relief appropriate to the circumstances.13 A reopening of the [396]*396record may be necessary to perfora these tasks.
F. Disparate Treatment
Six of the plaintiffs who were denied relief by the district court contend that the court erred in dismissing their individual claims of racially discriminatory treatment. Vicksburg argues that the district court erred in finding that Roosevelt Bunch and John Minor were victims of racial discrimination. The three-step order of proof for such claims was set out in McDonnell Douglas Corp. v. Green, 411 U.S. 792, 93 S.Ct. 1817, 36 L.Ed.2d 668 (1973). First, a plaintiff has the burden of proving a prima facie case of discrimination.14 If the plaintiff proves a prima facie case, the burden shifts to the defendant to articulate a legitimate, nondiscriminatory reason for the employee’s rejection. Finally, the plaintiff is entitled to prove that any such proffered reasons were pretexts for discrimination. “The ultimate burden of persuading the trier of fact that the defendant intentionally discriminated against the plaintiff remains at all times with the plaintiff.” Texas Department of Community Affairs v. Burdine, 450 U.S. 248, 253, 101 S.Ct. 1089, 1093, 67 L.Ed.2d 207, 215 (1981).
“Whatever importance this framework had below, ... by the time a fully-tried case reaches us on appeal, the parties’ showing at the preliminary levels of the framework is largely irrelevant.” EEOC v. Exxon Shipping Co., 745 F.2d 967, 972 (5th Cir.1984). “We need address only the propriety of the ultimate finding of discrimination vel non.” Id. Discriminatory intent is a factual matter subject to the clearly erroneous standard of Fed.R.Civ.P. 52(a). Pullman-Standard v. Swint, 456 U.S. 273, 102 S.Ct. 1781, 72 L.Ed.2d 66 (1982). Although this circuit previously treated a finding of discrimination or nondiscrimination as an “ultimate fact” subject to de novo appellate review, Rule 52(a) make no such distinction between “ultimate” and “subsidiary” facts. See id. at 285-87 & n. 15, 102 S.Ct. at 1788-89 & n. 15, 72 L.Ed.2d at 77-79 & n. 15. While the reason for the clearly erroneous rule rests in part on the trial judge’s ability to judge the demeanor and tone of witnesses’ testimony, “[t]he rationale for deference to the original finder of fact is not limited to the superiority of the trial judge’s position to make determinations of credibility.” Anderson v. Bessemer City, 470 U.S. 564, -, 105 S.Ct. 1504, 1512, 84 L.Ed.2d 518, 529 (1985). Judicial efficiency, gained by the avoidance of needless duplication in factfinding, is another product of the clearly erroneous rule. Id.
1. Lewis Fleming
Plaintiff Lewis Fleming presents the only claim of unlawfully discriminatory discharge. Fleming, a black patrolman discharged by the chief of police in 1977 just prior to the end of his six-month probationary period, claims that the district court erred in finding that he was not a victim of discrimination. The police chief’s version, believed by the court, was that Fleming had at times fallen asleep in his patrol car, failed to report for watch duty, and failed to move to the Vicksburg area as required. Fleming’s later attempt to find work in another county was allegedly delayed by the police chief’s unsolicited and unfavorable reference sent to Fleming’s prospective [397]*397employer. The court concluded that “The evidence is more persuasive in favor of [police chief] Holliday in that the evidence of his interference [with future employment] is insufficient to prove Fleming’s claim.”
We find no clear error in the district court’s resolution of conflicting testimony. Fleming admitted to falling asleep on duty once, although he claimed it occurred during the last fifteen minutes of a double shift. The police chief testified that Fleming had been caught napping on duty on other occasions, and that at least one white police officer had been similarly dismissed in part for sleeping on the job. Fleming testified that his failure to be present for watch duty was due to medical problems related to his wife’s pregnancy, but the police chief explained that Fleming’s shortcoming was not in his failure to attend but rather in his failure over a two-day period to either report directly to his watch commander or to explain the reason for his absences. Fleming did not challenge the police chief’s allegation that Fleming never moved to the Vicksburg area, contending only that he had “established an address” there.
2. Tom Harris
Plaintiff Tom Harris was initially hired as a patrolman in June 1969, and was promoted to sergeant in January 1973. In November 1976, Harris took an IPMA examination in order to qualify for promotion to lieutenant. He passed the examination, scoring a ninety-one, but did not receive the promotion. Police officers on other occasions received promotions after achieving lower scores, and Harris claims that the district court erred in determining that he was denied the promotion because of his race. Harris did not testify at trial but various documentary evidence was admitted in support of his claim.
We have no definite and firm conviction that the district court erred in its treatment of Harris’ disparate treatment claim. While Harris performed well on the IPMA examination, his score was second to that of plaintiff Herman Redick, who received the promotion to lieutenant. The November 1976 examination was the only one Harris attempted, and he introduced no evidence to show that there was more than one vacancy for the position of lieutenant at that time. Moreover, Harris had a checkered work history. He was suspended during parts of September and October 1976 for his participation in the attempted cover-up of an incident involving unauthorized shooting and a forced confession from a prisoner.15 At other times Harris has been charged by the police chief with delaying the report of an armed robbery, fleeing the scene after running into a parked car, and causing an automobile collision by violating department driving policy.
3. Willie James (“Bill”) Williams, Ar-tel Moore, and Cozell Gilliam
Plaintiffs Bill Williams, Artel Moore, and Cozell Gilliam argue that, contrary to the court’s conclusions, they were intentionally discriminated against when the police department ended its policy of [398]*398automatic promotion to sergeant for all who volunteered for motorcycle duty. These three black police officers were the first blacks to work as motorcycle officers. They were the first motorcycle officers denied the benefit of the automatic promotion. They claim that what appeared to be a neutral policy of discontinuing automatic promotions was in fact an intentional effort to deny blacks any advancement in the department.
Regardless of whether these three plaintiffs have made out a prima facie claim of discrimination, we find no clear error in the district court’s conclusion that they have not shown the articulated reason for the change to be mere pretext. The plaintiffs concede that the prior practice of automatic promotion produced too many sergeants and a top-heavy department. The police chief testified that one of the benefits of attaining the rank of sergeant, that of supervising others, had been largely lost because there were few patrolmen left to supervise. Although the change in policy came at an inopportune time for some, we cannot conclude that promotions had to continue to the point of worsening an already poorly structured department. Thus, Williams, Moore, and Gilliam have not met their ultimate burden of proving the ultimate issue of discrimination.16
4. Roosevelt Bunch and John Minor
Vicksburg argues that the district court erred by improperly inferring discriminatory intent, a requirement in a disparate treatment case, from the length of time Roosevelt Bunch and John Minor had worked without being promoted. Vicksburg contends that the district court failed to properly find that Bunch and Minor had been passed over for non-discriminatory reasons. Vicksburg’s argument has no merit. Vicksburg is not entitled to judgment as a matter of law merely because it has presented evidence on non-discriminatory intent. While Bunch and Minor may have produced no direct evidence of discriminatory motive, none is required. “[T]he evidence of subjective standardless decision-making by company officials, which is a convenient mechanism for discrimination, satisfies this requirement.” Boykin v. Georgia-Pacific Corp., 706 F.2d 1384, 1390 (5th Cir.1983), cert. denied, 465 U.S. 1006, 104 S.Ct. 999, 79 L.Ed.2d 231 (1984). Vicksburg was unable to persuade the district court that the pre-IPMA system of promotion was anything other than almost entirely standardless and subjective. The plaintiffs were not required to submit direct evidence of discriminatory intent, any more than any plaintiff must present direct evidence of a defendant’s state of mind. See U.S. Postal Service Board of Governors v. Aikens, 460 U.S. 711, 103 S.Ct. 1478, 75 L.Ed.2d 403 (1983). The court was entitled to infer intent from Bunch and Minor’s long wait for promotion while at least some whites were more quickly promoted, and to disbelieve Vicksburg’s proffered reasons.
G. Prejudgment Interest
Plaintiffs Bunch and Minor complain that the district court erred in failing to award prejudgment interest on their back pay awards. The court denied their request because of “the unliquidated nature of the claim, and the equities present____” They argue that such an [399]*399award is authorized under 28 U.S.C. § 1961 (providing for postjudgment interest) and is necessary to fashion relief which makes them whole. Prejudgment interest is available on back pay awards in Title VII cases. See Parson v. Kaiser Aluminum & Chemical Co., 727 F.2d 473, 478 (5th Cir.), cert. denied, 467 U.S. 1243, 104 S.Ct. 3516, 82 L.Ed.2d 824 (1984). The decision to award such interest is within the discretion of the district court, Taylor v. Philips Industries, Inc., 593 F.2d 783, 787 (7th Cir.1979), although this court has suggested in dicta that “interest” is an element that “should” be included in back pay. See Pettway, 494 F.2d at 264.
However, because Bunch and Minor have not appealed the judgment, they may not attack it here. The relevant notice of appeal listed the twelve other plaintiffs but omitted Bunch and Minor. “A notice of appeal shall specify the party or parties taking the appeal.” Fed.R.App.P. 3(c). Although this circuit, in the interests of fairness, gives a broad interpretation to the requirements of the rule, see Ayres v. Sears, Roebuck & Co., No. 84-1966, 789 F. 2d 1173 (5th Cir.1986), we will not suffer an appeal which does not at least “substantially comply” with its requirements. See G. E. Smith & Associates, Inc. v. Otis Elevator Co., 608 F.2d 126, 127 (5th Cir.1979). The error here was no minor irregularity or inadvertent drafting mistake; the plaintiffs’ brief carefully listed the appellants, but again omitted Bunch and Minor. The wording of the statement of facts leaves us with the inescapable conclusion that no appeal on behalf of Bunch or Minor was taken or intended.17 Accordingly, although the district court may exercise its discretion to award prejudgment interest to any additional back pay amounts for other plaintiffs as made necessary by our remand, the judgment as to Bunch’s and Minor’s awards is final.
H. Attorney’s Fees
The district court awarded the plaintiffs $22,928.50 in attorney’s fees under 42 U.S.C. § 2000e-5(k) and 42 U.S.C. § 1988. This amount was based on the court’s finding that the plaintiffs’ lead counsel legitimately expended 379.1 hours and his associate counsel 92 hours. These amounts reflected deductions made by the court for time expended in futile, unreasonable, or unnecessary labor. The court multiplied these hours by the rate of $65.00 per hour for lead counsel and $50.00 per hour for associate counsel. A final reduction of 25% was made upon the examination of the twelve factors of Johnson v. Georgia Highway Express, Inc., 488 F.2d 714 (5th Cir.1974). Plaintiffs object that this total amount is inadequate, because the court underestimated the measure of success achieved by them in the litigation and because the hourly rates awarded to the plaintiffs’ counsel were too low.18
The calculation of attorney’s fees is ordinarily left to the discretion of the district court. Claiborne v. Illinois Central Railroad, 583 F.2d 143 (5th Cir.1978) cert. denied, 442 U.S. 934, 99 S.Ct. 2869, 61 L.Ed.2d 303 (1979). Here, the district court in determining its reduction of 25% placed heavy reliance on the plain[400]*400tiffs’ failüre to completely achieve the relief they sought. Such consideration, one of the Johnson factors, is appropriate. See Hensley v. Eckerhart, 461 U.S. 424, 103 S.Ct. 1933, 76 L.Ed.2d 40 (1983). However, as a result of this appeal, the district court’s assumption that only two of the fourteen plaintiffs prevailed is open to substantial revision on remand. We therefore vacate the award of attorney’s fees in order to permit the district court to consider this factor in the further exercise of its discretion.19
III. CONCLUSION
We reverse that portion of the judgment denying plaintiffs relief on their disparate impact claims. We vacate the award of attorney’s fees. Affirming in all other respects, we remand for further proceedings not inconsistent with this Opinion.
REVERSED in part; VACATED in part; AFFIRMED in part; REMANDED.