
519 F.3d 264 (2008)
Sylvester McCLAIN, on his own behalf and on behalf of a class of similarly situated persons; Buford Thomas, on his own behalf and on behalf of a class of similarly situated persons; Patrick Ross, on his own behalf and on behalf of a class of similarly situated persons; Mary Thomas, on her own behalf and on behalf of a class of similarly situated persons; Eddie K. Mask, on his own behalf and on behalf of a class of similarly situated persons; Leroy Garner, on his own behalf and on behalf of a class of similarly situated persons; Sherry Calloway Swint, on her own behalf and on behalf of a class of similarly situated persons; Walter Butler, on his own behalf and on behalf of a class of similarly situated persons; also known as A; Florine Thompson, on her own behalf and on behalf of a class of similarly situated persons; Clarence Owens, on his own behalf and on behalf of a class of similarly situated persons; also known as C; Clifford R. Duirden, on his own behalf and on behalf of a class of similarly situated persons; Earl Potts, on his own behalf and on behalf of a class of similarly situated persons; Roald Mark, on his own behalf and on behalf of a class of similarly situated persons, Plaintiffs-Appellants-Cross Appellees,
v.
LUFKIN INDUSTRIES, INC., Defendant-Appellee-Cross Appellant.
No. 05-41417.
United States Court of Appeals, Fifth Circuit.
February 29, 2008.
*265 *266 *267 *268 *269 *270 *271 Teresa F. Demchak, Morris J. Baller (argued), Goldstein, Demchak, Baller, Borgen & Dardarian, Oakland, CA, Timothy Borne Garrigan, Stuckey, Garrigan & Castetter, Nacogdoches, TX, for Plaintiffs-Appellants-Cross-Appellees.
Douglas E. Hamel (argued), Christopher Velle Bacon, Vinson & Elkins, Houston, TX, for Lufkin Industries, Inc.
Before JONES, Chief Judge, and HIGGINBOTHAM and CLEMENT, Circuit Judges.
EDITH H. JONES, Chief Judge:
In this complex Title VII class action against Lufkin Industries, Inc. ("Lufkin"), African-American plaintiffs allege that Lufkin's practice of delegating subjective decision-making authority to its managers with respect to initial assignments and promotions disparately affected them. After a bench trial, the district court issued a judgment in favor of the employees. After sifting through numerous issues, we reach results that are unfortunately inconclusive of the litigation. We affirm in part, reverse in part, and vacate and remand in part.

I. FACTUAL AND PROCEDURAL BACKGROUND
Lufkin, a large manufacturing corporation located in Lufkin, Texas, is divided into four production divisions: Foundry, Trailer, Oil Field, and Power Transmission. The company employs approximately 1,500 hourly and salaried workers, and the hourly workers have been unionized for many years.
Only two of the representative plaintiffs in this class action filed EEOC complaints. Sylvester McClain ("McClain"), the named plaintiff, began working in Lufkin's Trailer division in 1972. In January 1995, he complained to the EEOC that his supervisor, Arden Jinkins ("Jinkins"), had discriminated against him based on his race. Among other things, McClain complained that Jinkins tried to have him demoted. Buford Thomas ("Thomas"), a Lufkin employee since 1979, filed his EEOC charge in February 1997, a year after he was allegedly constructively discharged. Thomas complained of being denied promotional and training opportunities because of his race while working in the Power Transmission and Oil Field divisions. The EEOC issued right-to-sue letters on both charges.
McClain and Thomas sued Lufkin for employment discrimination in violation of Title VII and 42 U.S.C. § 1981. The plaintiffs asserted that systematic racial discrimination pervades Lufkin's initial job assignments, training, promotions, and compensation. The district court certified the plaintiffs' disparate-impact claims as a class action involving 700 current and former Lufkin employees. The class was described as:

*272 All Black persons employed for any period of time by defendant Lufkin Industries on or after March 6, 1994, to date, whose compensation, remuneration, benefits, job assignments, promotional opportunities, career advancements and other terms and conditions of employment have been, may have been, or may become, adversely affected by defendant Lufkin Industries' past or present systems of administering hiring, wages, salaries, job assignments, training, evaluations, promotions, demotions, terminations, layoffs, recalls, and rehires.
McClain v. Lufkin Indus., Inc., 187 F.R.D. 267, 277-78 (E.D.Tex.1999). The court, however, declined to certify a disparate treatment class. Two claims went to trial: (1) discrimination against blacks in Lufkin's assignment of newly hired employees; and (2) racially discriminatory promotion practices that rested on largely subjective decision-making criteria carried out by a largely white supervisory corps.
Protracted pretrial proceedings in this case included two class certification hearings, two interlocutory appeals to this court, and a two-year mediation effort. When the case finally went to bench trial, the court strictly limited each party to twenty hours for the presentation of its case. Ultimately, the district court found that Lufkin's practice of delegating subjective decision-making authority to its white managers with respect to initial assignments and promotions resulted in a disparate impact on black employees in violation of Title VII. The court awarded the plaintiffs over $3.4 million in back pay, as well as attorneys' fees and injunctive relief. Both parties appeal.

II. DISCUSSION
Lufkin contends that the named plaintiffs failed to exhaust EEOC administrative remedies and lack standing to represent the class. Lufkin also contends that the district court erred in finding that Lufkin's promotion practices are subjective and incapable of separation for analysis and that they had a statistically significant disparate impact on black employees. Lufkin challenges the court's calculation of the back pay award according to a class-wide formula. Finally, Lufkin asserts that the cumulative effect of various errors, including the limited presentation of evidence, requires us to vacate the judgment.
For their part, the plaintiffs argue that the district court erred in refusing to certify a disparate treatment class, in failing to award appropriate injunctive relief, and in reducing their attorneys' fees. We turn first to Lufkin's contentions.

A. Lufkin's Arguments

1. Failure to Exhaust EEOC Remedies
As a threshold matter, Lufkin argues that the district court should have dismissed the plaintiffs' initial-assignment and promotion claims for failure to exhaust administrative remedies and for lack of standing to represent a broadly defined class. Failure to exhaust is not a procedural "gotcha" issue. It is a mainstay of proper enforcement of Title VII remedies. Lufkin contends that McClain and Thomas complained to the EEOC about their individual disparate treatment by the company, but not about their hiring nor about any neutral employment practices on which a disparate-impact case depends. The scope of their administrative claims governs the scope of the class claims. Vuyanich v. Republic Nat'l Bank, 723 F.2d 1195, 1201 (5th Cir.1984); Evans v. U.S. Pipe & Foundry Co., 696 F.2d 925, 929 (11th Cir.1983). Consequently, Lufkin asserts, the EEOC was never presented with disparate-impact class claims concerning Lufkin's hiring and promotional practices, *273 and the administrative process was circumvented.
The district court ruled that plaintiffs had exhausted their administrative remedies via McClain's January 1995 letter to the EEOC. See 29 C.F.R. § 1601.12(b); Fellows v. Universal Rests., Inc., 701 F.2d 447, 451 (5th Cir.1983). The court also held that a contemporary administrative proceeding pertaining to Lufkin by the Office of Federal Contract Compliance Programs ("OFCCP") sufficiently fulfilled the purposes of exhaustion. This court reviews de novo the district court's conclusion concerning exhaustion. See Pacheco v. Mineta, 448 F.3d 783, 788 (5th Cir.), cert. denied, ___ U.S. ___, 127 S.Ct. 299, 166 L.Ed.2d 154 (2006).
Title VII requires employees to exhaust their administrative remedies before seeking judicial relief. Id. Private sector employees must satisfy this requirement by filing an administrative charge with the EEOC. Id. at 788 n. 6. The charge enables the EEOC to investigate and, if appropriate, negotiate a resolution with an employer. Only after administrative efforts terminate may the employee sue the employer in federal court.
Courts should not condone lawsuits that exceed the scope of EEOC exhaustion, because doing so would thwart the administrative process and peremptorily substitute litigation for conciliation. Nevertheless, competing policies underlie judicial interpretation of the exhaustion requirement. See id. at 788-89. On one hand, the scope of an EEOC charge should be liberally construed for litigation purposes because Title VII "was designed to protect the many who are unlettered and unschooled in the nuances of literary draftsmanship." Sanchez v. Standard Brands, Inc., 431 F.2d 455, 465 (5th Cir. 1970). On the other hand, the "primary purpose of Title VII is to trigger the investigatory and conciliatory procedures of the EEOC, in [an] attempt to achieve non-judicial resolution of employment discrimination claims." Pacheco, 448 F.3d at 788-89. To reconcile these policies, this court construes an EEOC complaint broadly but in terms of the administrative EEOC investigation that "can reasonably be expected to grow out of the charge of discrimination." Sanchez, 431 F.2d at 466. We use a "fact-intensive analysis" of the administrative charge that looks beyond the four corners of the document to its substance. Id. In sum, a Title VII lawsuit may include allegations "like or related to allegation[s] contained in the [EEOC] charge and growing out of such allegations during the pendency of the case before the Commission." Id.
Among this court's numerous rulings on exhaustion of EEOC claims, we find most relevant the recent Pacheco opinion, which held that an employee failed to exhaust a disparate-impact claim because his EEOC charge alleged only disparate treatment and identified no neutral employment policy. 448 F.3d at 792. Although Pacheco's administrative charge complained that he had not been promoted because of racial discrimination, his subsequent lawsuit alleged both disparate treatment and disparate impact. Id. at 786-87. This court affirmed the dismissal of the disparate-impact allegations because:
a disparate-impact investigation could not reasonably have been expected to grow out of Pacheco's administrative charge because of the following matters taken together: (1) it facially alleged disparate treatment; (2) it identified no neutral employment policy; and (3) it complained of past incidents of disparate treatment only.
Id. at 792.
In this case, both the district court and the plaintiffs rely principally on *274 McClain's January 1995 letter to establish administrative exhaustion. Like Pacheco, McClain specifically complained to the EEOC of disparate treatment and past incidents of discrimination against himself. His three-page letter to the EEOC describes "discriminatory treatment that I have been receiving for some time," and "discriminatory acts against me by Mr. Jinkins." McClain alleged that Jinkins, his supervisor, racially discriminated against him and tried to have him demoted or fired on false charges of unsatisfactory performance.
McClain's letter nowhere refers to any neutral employment policy of Lufkin. Yet, according to Pacheco, "the cornerstone of any EEO[C] disparate-impact investigation" is a neutral employment policy. 448 F.3d at 792. Plaintiffs argue that a disparate-impact investigation could have grown out of McClain's letter because he alluded to a "cultural problem" that extended to all parts of Lufkin's business. A "cultural problem," however, is a vague term that cannot be understood as a neutral employment policy. See, e.g., id. at 790. Compare Marshall v. Fed. Express Corp., 130 F.3d 1095, 1098 (D.C.Cir.1997) ("A vague or circumscribed EEOC charge will not satisfy the exhaustion requirement for claims it does not fairly embrace."), with Gomes v. Avco Corp., 964 F.2d 1330, 1335 (2d Cir.1992) (disparate-impact investigation "would reasonably have flowed" from an EEOC complaint that referenced an eight-year track to promotion). McClain's letter not only failed to identify any neutral employment policy, but also said nothing about discriminatory hiring at Lufkin.
This limited interpretation of McClain's letter is confirmed by the actual scope of the EEOC's investigation, which is clearly pertinent to an exhaustion inquiry. See Fine v. GAF Chem. Corp., 995 F.2d 576, 578 (5th Cir.1993); Fellows, 701 F.2d at 451. Responding to the January 1995 letter, the EEOC sent McClain a proposed formal charge of discrimination in August 1996, in which the agency summarized his claim as follows:
I have been subjected to different terms and conditions of employment by being denied comparable training, access to supplies and equipment needed to do a satisfactory job; given unsatisfactory evaluations.
The charge then repeats McClain's complaint of demotion. The plaintiffs also cite another of McClain's written statements to the EEOC, in which he suggests that other evidence could be disclosed to support his discrimination claim. In context, this sentence refers only to Lufkin's disparate treatment of McClain alone.
The district court attempted to fortify its conclusion that exhaustion occurred by taking into account an investigation by the OFCCP into "similar claims to those now before the court." The court seemed to think that an investigation by another federal agency can exhaust claims that must be handled by the EEOC and that Lufkin was effectively notified of its exposure to disparate-impact claims by responding to the OFCCP investigation. The district court cited no authority in support of its exhaustion bootstrapping, and we are aware of none. Further, no such Title VII shortcut to exhaustion or notification exists. Since 1970, the caselaw has explained that "the `scope' of the judicial complaint is limited to the `scope' of the EEOC investigation which can reasonably be expected to grow out of the charge of discrimination." Sanchez, 431 F.2d at 466 (emphasis added); see also Pacheco, 448 F.3d at 792 ("[T]he plaintiff's administrative charge will be read somewhat broadly, in a fact-specific inquiry into what EEOC investigations it can reasonably be *275 expected to trigger." (emphasis added)); Fellows, 701 F.2d at 450-51. The district court erred by utilizing OFCCP's investigation as a basis for inferring EEOC administrative exhaustion.
Although McClain's EEOC complaint and the OFCCP investigation failed to exhaust the employees' class claims, Buford Thomas's EEOC complaint carries part of the requisite burden. Thomas alleged to the EEOC that he was constructively discharged, denied promotional and training opportunities, and overloaded with work because of his race. He specifically stated that "[r]espondent has similarly discriminated against other black African Americans." Thomas's complaint, viewed in light of the recent Pacheco decision, presents a close question of exhaustion directed at a discriminatory, albeit neutral, company policy authorizing subjective promotion decisions. We conclude, however, that exhaustion was sufficient. Significantly, Lufkin did not contend otherwise in the trial court.[1]
Lufkin, instead, forcefully urged that the class failed to exhaust claims concerning Lufkin's alleged discriminatory assignment of newly hired black employees to the Foundry division. Hourly work in the Foundry division is hot and heavy to a far greater extent than in the company's other production divisions. But neither Thomas nor McClain, each with twenty or more years at Lufkin, had worked in the Foundry division and neither man could or did complain to the EEOC about Foundry hiring practices. We are persuaded that the EEOC would not reasonably have investigated discriminatory assignment of new Foundry division employees based on either McClain's or Thomas's charge. Eastland v. Tenn. Valley Auth., 714 F.2d 1066, 1067-68 (11th Cir.1983) (class representatives could not assert initial assignment claims because all had been hired years before); Evans v. U.S. Pipe & Foundry Co., 696 F.2d 925, 929 (11th Cir. 1983) (EEOC investigation limited to promotion and harassment). Because of this deficiency, we must vacate the judgment awarding damages and injunctive relief against Lufkin based on discriminatory initial assignments to the Foundry division.[2]
Lufkin's liability will next be examined in regard to the class's promotion-discrimination claim.

2. Failure to Isolate a Specific Employment Practice
The district court identified Lufkin's subjective decision-making process in awarding promotions as the employment practice that caused a disparate impact on black employees. To establish a prima facie case of discrimination under a disparate-impact theory, a plaintiff must show: (1) an identifiable, facially neutral personnel policy or practice; (2) a disparate effect on members of a protected class; and (3) a causal connection between the two. Watson v. Fort Worth Bank & Trust, 487 U.S. 977, 994, 108 S.Ct. 2777, *276 101 L.Ed.2d 827 (1988). Ordinarily, a plaintiff must demonstrate that each particular challenged employment practice causes a disparate impact. Yet, Title VII provides that "if the complaining party can demonstrate to the court that the elements of [the employer's] decision making process are not capable of separation for analysis, the decision making process may be analyzed as one employment practice." 42 U.S.C. § 2000e-2(k)(1)(B)(i).
Lufkin challenges two factual findings underlying the court's liability determination: that its decision-making process is subjective; and that its decision-making process could not be separated for analysis into components that were objective and non-racially biased. We address each in turn.

a. Subjective Decision Making
Lufkin argues that its promotion system is in fact overwhelmingly objective, and that the district court's finding of subjective decision making lacks support. We review this finding for clear error. See Kona Tech. Corp. v. S. Pac. Transp. Co., 225 F.3d 595, 601 (5th Cir.2000).[3]
In Watson, the Supreme Court defined subjective decision making as employment decisions "based on the exercise of personal judgment or the application of inherently subjective criteria." 487 U.S. at 988, 108 S.Ct. 2777. The Court indicated that a system which incorporates a mixture of subjective and objective criteria should generally be treated as subjective. Id. at 989, 108 S.Ct. 2777 ("However one might distinguish `subjective' from `objective' criteria, it is apparent that selection systems that combine both types would generally have to be considered subjective in nature.").
At Lufkin, promotions within the hourly ranks are putatively governed by a Collective Bargaining Agreement ("CBA") between Lufkin and three unions. Under the CBA, the company must post bid sheets for each new hourly opening. Seniority is the main criterion for promotion. However, plaintiffs offered evidence that promotions are not rigidly awarded according to seniority. Class members Sylvester McClain and Florine Thompson testified that they were personally bypassed for promotion in favor of a less senior white employee. Plaintiffs presented additional evidence that approximately half of all promotions were not awarded to the most senior bidder.
Moreover, the Collective Bargaining Agreement ("CBA") contains an ability clause that allowed Lufkin to fill positions on the basis of ability, regardless of seniority. The evidence indicates that ability determinations were not governed by objective standards. Paul Perez, Lufkin's Vice President of Human Resources, agreed that the ability determination was subjective. McClain testified that supervisors did not always truly evaluate ability when awarding promotions under the ability clause, but simply gave the position to the candidate they favored. Billy Webb, the union's chief spokesman, testified that the union had taken issue with the ability provision in past contract negotiations because it did not think that the ability clause was always administered fairly. The CBA also provides for a ten-day trial period following promotion. According to the testimony of one of its managers, Lufkin has no written guidelines or formal tests for determining which employees pass this trial period.
*277 Plaintiffs also offered evidence that Lufkin permitted its managers to apportion training opportunities subjectively, a process that disadvantaged black employees who sought promotions. Perez testified that the CBA does not govern employees' daily work assignments, and he acknowledged that daily job assignments are not made on the basis of seniority. Perez testified that there are no written policies determining who is to receive on-the-job training, and Lufkin does not track how such training is allocated among employees. In addition, McClain testified that white employees were given more training in areas that were relevant to the jobs he sought. McClain explained that when "white managers and supervisors . . . see a man they want to put on a particular job, . . . they'll tap him" for training after his shift, or for external training. According to McClain, the employee who received the extra training would be the most qualified and would therefore receive the promotion once the job became available.
The district court also heard testimony that Lufkin's allegedly objective measures for determining which employees were eligible to bid, such as attendance and discipline records, are subject to variance and manipulation. Lufkin has a computer program that tracks attendance, but both McClain and Thompson testified that the system was manipulable. If an employee was absent or tardy and the supervisor did not want the employee to lose credit, Thompson stated that the supervisor could non-schedule the employee or use the employee's vacation days to skew the records. With respect to discipline records, Steve Reynolds, a Lufkin supervisor, testified that there are no written criteria for determining when a rule violation should be "written up." He stated that this decision is left to individual supervisors.
The evidence also supported that Lufkin engaged in subjective decision making when awarding promotions in the salaried ranks. Salaried positions are not governed by the CBA, and company managers admitted that they were unaware of any guidelines, criteria, or documentation for the process of making promotions to salaried positions. Rather, most promotions in the salaried ranks are awarded through an interview process.[4]
In light of this evidence, we are not left with the definite and firm conviction that the district court erred in finding subjective decision making in Lufkin's promotion system. See United States v. U.S. Gypsum Co., 333 U.S. 364, 395, 68 S.Ct. 525, 92 L.Ed. 746 (1948). Although Lufkin offered some testimony during the bench trial that would tend to refute the court's finding, it was within the province of the district court to accord this testimony less credibility than that of the class members and their experts. "The reviewing court oversteps the bounds of its duty under Rule 52(a) if it undertakes to duplicate the role of the lower court." Anderson v. City of Bessemer City, 470 U.S. 564, 573, 105 S.Ct. 1504, 84 L.Ed.2d 518 (1985). Accordingly, we cannot say the court's finding of subjective decision making in promotions amounted to clear error.

b. Not Capable of Separation for Analysis
Lufkin also challenges the district court's finding that its promotion practices *278 are not capable of separation for review. Lufkin argues that if the court had isolated the objective factors in promotions  e.g. Lufkin's bidding practices and seniority  the court could not have found a discriminatory impact. As explained above, Title VII permits a plaintiff to demonstrate that the elements of the employer's decision-making process are not capable of separation for analysis and thus that the process should be analyzed as one employment practice. 42 U.S.C. § 2000e-2(k)(1)(B)(i). This court has not addressed the precise conditions under which employment practices are "not capable of separation for analysis." But "where a promotion system uses tightly integrated and overlapping criteria, it may be difficult as a practical matter for plaintiffs to isolate the particular step responsible for the observed discrimination." See Munoz v. Orr, 200 F.3d 291, 304 (5th Cir.2000). Some guidance is also provided by trial court decisions interpreting the provision. In Stender v. Lucky Stores, Inc., the district court held:
Where the system of promotion is pervaded by a lack of uniform criteria, criteria that are subjective as well as variable, discretionary placements and promotions, the failure to follow set procedures and the absence of written policies or justifications for promotional decisions, the court is not required to "pinpoint particular aspects of [the system]" that are unfavorable to [the protected group].
803 F.Supp. 259, 335 (N.D.Cal.1992) (citation omitted); see also Butler v. Home Depot, Inc., No. C-94-4335 SI, 1997 WL 605754, at *13 (N.D.Cal. Aug. 29, 1997) (unreported) (where employer delegated decisions to store managers who made subjective judgments about candidate's qualifications without written criteria, decision-making process not capable of separation for analysis); Schallop v. N.Y. State Dept. of Law, 20 F.Supp.2d 384, 402 (N.D.N.Y.1998) (entire process may be characterized as a single employment practice when employment decisions are made based on variable, subjective criteria); Bannister v. Dal-Tile Int'l, Inc., No. 3:02-CV-2498, 2003 WL 21145739, at *2 (N.D.Tex. May 14, 2003) (plaintiff not required to pinpoint specific employment practices where the factors of a defendant's decision-making process are "so interwoven that they are incapable of separation").
There is no indication that the district court applied incorrect legal principles in determining that Lufkin's practices were incapable of separation. This finding of fact must be reviewed for clear error. See Kona, 225 F.3d at 601. Lufkin lists various ways in which its employment practices were analytically separable, but the court's express findings preclude separation according to those factors.
Lufkin argues, for example, that the plaintiffs' expert could have separated the challenged employment practices from its legitimate seniority system. The expert included in his analysis numerous promotions that contributed to the statistical shortfall in black promotions, even though these jobs were indisputably awarded to the most senior candidate. This argument ignores the district court's finding that Lufkin affords management considerable discretion in deciding whether to follow seniority in promotions. Plaintiffs could not statistically analyze the actual practice they challenge  subjective and discretionary application of the seniority provisions  by excluding promotion based on seniority. Seniority, the court found, was likely to have been irrelevant to the promotion.
Lufkin also contends that the plaintiffs should have separated out instances in which candidates were properly denied *279 promotions because of unsatisfactory attendance. This argument, too, runs afoul of the court's finding that managers have substantial discretion in applying attendance rules. In such a system, a denial of promotion for poor attendance is not helpful to Lufkin where promotions may also have been awarded following non-uniform interpretation of employee attendance rules.
Finally, Lufkin contends that its "paper bid sheets provided additional information that plaintiffs could have separated for analysis."[5] To the contrary, the district court rejected the bid data, which Lufkin prepared for purposes of this litigation, as unreliable and incomplete; ample evidence supports this finding.
Lufkin has not suggested any viable way, consistent with the court's findings, in which the plaintiffs could have separated the promotion criteria for review nor has it shown the district court clearly erred in so finding.

3. Statistically Significant Disparate Impact in Promotions
Lufkin maintains that the plaintiffs failed to demonstrate a statistically significant disparate impact against black employees in promotions. At trial, plaintiffs provided statistical evidence of discrimination through the report of their expert, Dr. Richard Drogin. After constructing hypothetical pools of employees who would be eligible for promotion, Dr. Drogin found that during the class period, black employees received 127 fewer hourly promotions and 8.85 fewer salaried promotions than should have been expected given their representation in these pools. Dr. Drogin determined that these differences were statistically significant at 7.61 standard deviations for hourly promotions and at 2.02 standard deviations for salaried promotions. In rebuttal, Lufkin offered the statistical analysis of Dr. Mary Baker. Dr. Baker conducted her calculations using bid data from Lufkin's paper bid sheets, and concluded that there was no statistically significant disparity in the promotion of blacks to hourly or salaried positions. Faced with this battle of experts, the district judge credited the testimony of Dr. Drogin over that of Dr. Baker.
Our role in reviewing this decision is limited. An appellate court owes great deference to the findings of the trial court with respect to duly admitted expert testimony. Cleveland ex rel. Cleveland v. United States, 457 F.3d 397, 407 (5th Cir. 2006). We review for abuse of discretion the district court's decision to credit one expert over another. Id. And we reverse a district court's factual finding that an employment decision was the product of unlawful discrimination only if it is clearly erroneous. See Bazemore v. Friday, 478 U.S. 385, 398, 106 S.Ct. 3000, 92 L.Ed.2d 315 (1986); Anderson v. City of Bessemer City, 470 U.S. 564, 573, 105 S.Ct. 1504, 84 L.Ed.2d 518 (1985).
With these standards in mind, we turn to Lufkin's specific contentions. First, Lufkin argues that Dr. Drogin's analysis is legally insufficient because he did not use "actual" applicant lists and bid *280 sheets to: (1) construct the availability pools; (2) consider potentially non-discriminatory explanations for the promotions; and (3) factor in qualifications of potential applicants. Lufkin is correct, of course, that actual applicant flow data are superior, and should be used if available. See Anderson v. Douglas & Lomason Co., 26 F.3d 1277, 1286-87 (5th Cir.1994). But as discussed above, the district court expressly found that the bid data were incomplete and unreliable, noting that more than half of the promotions were missing from the bid database which Lufkin prepared in anticipation of this litigation. Where actual data are unreliable, courts often permit parties to analyze potential applicant flow data. See, e.g., Malave v. Potter, 320 F.3d 321, 326-27 (2d Cir.2003); Berger v. Iron Workers Reinforced Rodmen Local 201, 843 F.2d 1395, 1414 (D.C.Cir.1988); Hameed v. Iron Workers Local 396, 637 F.2d 506, 512 n. 6 (8th Cir.1980); Lewis v. Bloomsburg Mills, Inc., 773 F.2d 561, 568 (4th Cir.1985). The district court did not err in allowing plaintiffs to do so in this case.
Lufkin argues that even if the bid sheets were unavailable, Dr. Drogin's regression analysis would still be insufficient because his hypothetical applicant pools do not take into account other minimum qualifications of applicants, such as education. However, in selecting an appropriate pool and performing regression analysis in Title VII cases, the Supreme Court has taught that a plaintiff's regression analysis need not include "all measurable variables." See Bazemore, 478 U.S. at 400, 106 S.Ct. 3000 ("[I]t is clear that a regression analysis that includes less than `all measurable variables' may serve to prove a plaintiff's case."); see also Mozee v. Am. Commercial Marine Serv. Co., 940 F.2d 1036, 1045 (7th Cir.1991). 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. Bazemore, 478 U.S. at 400, 106 S.Ct. 3000. We are satisfied that Dr. Drogin's regression analysis was sufficiently refined for plaintiffs to meet this burden.
Finally, Lufkin argues that a disparity in salaried promotions of only 2.02 standard deviations does not support the district court's finding of disparate impact. This court has rejected the contention that a disparity of two or three standard deviations is categorically insufficient to support an inference of adverse impact. See Rendon v. AT&T Techs., 883 F.2d 388, 397-98 (5th Cir.1989).[6] And Lufkin has not persuasively explained why a standard deviation of this magnitude should be accorded reduced significance under the particular circumstances of this case. We therefore affirm the district court's finding of a statistically significant disparate impact in promotions.

4. Class-Wide Back-Pay Formula
Lufkin also challenges the class-wide back-pay award. The district court's calculation of a back pay award is reviewed for clear error. Shipes v. Trinity Indus., 987 F.2d 311, 316-17 (5th Cir.1993).

a. Class-Wide Formula or Individual Hearings
Lufkin complains that the district court erred by using a formula to calculate the award rather than computing damages on an individual basis. The complexity of the case is the determining factor *281 in what method the district court should utilize to formulate a back-pay award. Pettway v. Am. Cast Iron Pipe Co., 494 F.2d 211, 261 (5th Cir.1974). Whenever possible, back pay should be awarded individually and tailored to the actual victims of discrimination. United States v. U.S. Steel Corp., 520 F.2d 1043, 1055-56 (5th Cir.1975). If the class is small, the time period short, or the effect of the discrimination straightforward, individual determinations of each claimant's position but for the discrimination are possible. Pettway, 494 F.2d at 261. If, however, the class is large, the promotion or hiring practices are ambiguous, or the illegal practices continued over an extended period of time, a class-wide approach to the measure of back pay may be necessary. Id.; see also Shipes, 987 F.2d at 318.
In this case, the district court concluded that the size of the class and the inherent uncertainty of the individual claims contraindicates the use of an individualized approach. We agree. We are not persuaded that the district court could "easily" make individualized inquiries for each of the more than 700 plaintiffs in this case, as Lufkin contends. Further, as in Pettway, there is no practical way to determine through individual hearings which jobs the class members would have bid on and obtained but for the discriminatory procedures Lufkin had in place. See Pettway, 494 F.2d at 260. Class members outnumber promotion vacancies; jobs become available over time; the vacancies involve different pay rates; and a determination of who was entitled to a vacancy would have to be made by an evaluation of seniority and ability at that time. Id. (citing identical factors in approving the formula approach).[7] "[W]here employees start at entry level jobs in a department and progress into a myriad of other positions and departments on the basis of seniority and ability over an extended period of time, exact reconstruction of each individual claimant's work history, as if discrimination had not occurred, is not only imprecise but impractical." Id. at 262. An individualized process of determining actual damages for each plaintiff in this case would result in the "quagmire of hypothetical judgments" that courts should avoid. Id. at 260. Accordingly, the district court neither abused its discretion nor clearly erred in adopting the formula-driven approach.

b. Specific Methodology
While Lufkin levies various attacks on the district court's methodology for determining the back-pay award, these need not all be considered. With the elimination of a finding of class discrimination in initial assignments to the Foundry, the damage award must be vacated and remanded.
On remand, the district court will be dealing solely with damages attributable to approximately 127 lost promotions in hourly pay grades and nine lost salaried employment promotions. The accepted way to apportion damages among a class of plaintiffs who outnumber the lost promotion spots is to compute the total additional wages attributable each year to each promotion and divide the value among the class members. See United States v. City of Miami, 195 F.3d 1292, 1299-1302 (11th Cir.1999); Dougherty v. Barry, 869 F.2d 605, 614-15 (D.C.Cir.1989) (Ginsburg, J.); Hameed v. Iron Workers Local 396, 637 F.2d 506, 520-21 (8th Cir.1980). The district *282 court should adapt this method with whatever modifications will both expediently and fairly apportion the lost wages among class members working in the multiple divisions of Lufkin.
What the court may not do is return to Dr. Drogin's lost wages calculations given our disposition of this case. Dr. Drogin estimated annual hourly wage disparities between black and white workers and black and non-white workers and made a similar racial comparison for salaried workers. The conclusions in this section of his report were intended to demonstrate the systemic effects of racially discriminatory Foundry assignments throughout workers' careers. Whether or not such conclusions would be supportable for both hiring and promotion claims, they do not pertain to the class claim that is now limited to lost promotions. Dr. Drogin's figures would come close to compensating each class member for the full value of lost promotions, where plainly each member had at best a possibility of progressing up the ladder. The district court is free to consider any additional evidence that the parties may offer on this issue.

5. Limitation on the Presentation of Evidence and Trial Location
Lufkin argues that given the complexity of the issues involved in this case, the district court's imposition of rigid time limits on the presentation of evidence deprived Lufkin of a fair trial. A district court has broad discretion in managing its docket and structuring the conduct of a trial. Sims v. ANR Freight Sys., Inc., 77 F.3d 846, 849 (5th Cir.1996). It may maintain the pace of the trial by setting time limits on counsel. Id. Moreover, a judge has special latitude in applying time limits in a bench trial, since the court often has become familiar with the case long before trial begins and can readily comprehend the evidence presented. Id. at 850. Nevertheless, discretion has its limits. See id. at 849; see also Kelly v. Boeing Petroleum Servs., Inc., 61 F.3d 350, 358 (5th Cir. 1995). "When the manner of the presentation of information . . . is judicially restricted to the extent that the information becomes incomprehensible then the essence of the trial [is] destroyed." Sims, 77 F.3d at 849.
In this case, we do not doubt that it was difficult for Lufkin to mount a defense against generalized claims of subjective decision making  claims that implicated all of its divisions and spanned almost a decade  in the mere twenty hours the district court allowed each side. But even if the strict time limits amounted to an abuse of discretion, the district court's error is presumed harmless until shown to be prejudicial. See Ruiz v. Estelle, 679 F.2d 1115, 1129 (5th Cir.1982); see also Sims, 77 F.3d at 849-50 (declining to reverse where the complaining party did not establish there was a reasonable probability that the outcome of the case would be different upon retrial). Lufkin has not persuaded us that it suffered reversible prejudice. Lufkin's related claim of "cumulative error" fails because it is essentially rendered moot by the pervasive effect of our appellate ruling.

B. Plaintiffs' Arguments

1. Disparate Treatment Class Certification
Plaintiffs contend that the district court erred in denying class certification of their 42 U.S.C. § 1981 disparate-treatment claim seeking declaratory, injunctive, and equitable back pay.[8]See Allison *283 v. Citgo Petroleum Corp., 151 F.3d 402, 415-16 (5th Cir.1998) (equitable monetary relief, i.e., back pay, available in (b)(2) class actions). The district court declined to certify the class under Rule 23(b)(2) because individual claims for monetary relief would have predominated, and it concluded that the class representatives would be "inadequate" if they dropped the class members' demand for compensatory and punitive damages in order to protect the "predominance" of nonmonetary claims. See FED.R.CIV.P. 23(b)(2). This court reviews the district court's class-certification decision for abuse of discretion. See Allison, 151 F.3d at 408. Whether the court applied the correct legal standard in reaching its decision is reviewed de novo. Id.
The district court did not abuse its discretion. See Pegues v. Miss. State Employment Serv., 699 F.2d 760, 763 (5th Cir.1983) ("Implicit in this deferential standard of review is the recognition of the essential factual nature of the certification inquiry and the district court's inherent power to manage and control pending litigation."). Motivated by Zachery v. Texaco Exploration & Production, Inc., 185 F.R.D. 230 (W.D.Tex.1999), the district court expressed concern about the plaintiffs' disavowal of monetary damages. In Zachery, the putative class representatives also dropped their demand for compensatory and punitive damages in order to achieve Rule 23(b)(2) certification. Id. at 233. As a result, class members would not have had the right to opt out of the class and might be barred from bringing individual damage claims. Id. at 243 (citing Cooper v. Fed. Reserve Bank of Richmond, 467 U.S. 867, 104 S.Ct. 2794, 81 L.Ed.2d 718 (1984)). Noting this serious conflict of interest, the court refused to impose upon the class members the decision by named plaintiffs to forfeit the compensatory and punitive damages claim. Id. at 244-45. We agree with Zachery and with the district court's conclusion here that if the price of a Rule 23(b)(2) disparate treatment class both limits individual opt outs and sacrifices class members' rights to avail themselves of significant legal remedies, it is too high a price to impose. There was no error, much less abuse of discretion, in this certification denial.

2. Vague Remedial Injunction
Plaintiffs argue that the district court's remedial injunction lacks specificity, fails to remedy the discriminatory exercise of subjective decision-making practices, and includes no provision to ensure Lufkin's compliance. Lufkin agrees that the injunction is unenforceable for lack of specificity, but urges us to reject the additional injunctive relief that plaintiffs now request. We review a district court's fashioning of injunctive relief for abuse of discretion. Peaches Entm't Corp. v. Entm't Repertoire Assocs., Inc., 62 F.3d 690, 693 (5th Cir.1995).
The injunction at issue is identical to one the district court included in a preliminary order in January 2005. Lufkin appealed the injunction immediately after the preliminary order. We dismissed the appeal, stating that "[b]efore this matter is ripe for appellate review, the district court must identify the specific steps the defendant must take to implement and comply with the injunction." Despite this instruction, the district court included the original injunction verbatim in the final amended judgment.
The court's injunction lacks the detail required under Federal Rule of Civil Procedure 65(d). The injunction includes such *284 vague directives as "cease and desist all racially biased assignment and promotion practices," "create and implement a program to ensure that black employees receive an equitable proportion of promotions," and "take all necessary steps to remedy the effects of past discrimination." An order framed in these broad generalities fails to afford notice to Lufkin of its proscribed or required conduct and is therefore unenforceable. We vacate and remand for the court to try again.
This task will not be simple. Where, as here, Title VII does not require plaintiffs to pinpoint the specific practices that caused the discriminatory effect, it is especially difficult to craft an adequate remedial order that will eliminate discrimination without hobbling Lufkin's legitimate promotion policies. We leave to the district court the task of reviewing afresh the propriety of the injunction, and if it is found necessary, of balancing plaintiffs' requests for stronger measures to ensure Lufkin's compliance with the imprecision of the liability finding.

3. Attorneys' Fees
Plaintiffs contend that the district court abused its discretion by reducing their fees without conducting lodestar and Johnson analyses or making factual findings to support the reduction. A district court's determination of attorneys' fees is reviewed for abuse of discretion, and the findings of fact supporting the award are reviewed for clear error. Von Clark v. Butler, 916 F.2d 255, 258 (5th Cir.1990).
The first step in determining statutorily authorized attorneys' fees is to calculate a "lodestar" amount by multiplying the number of hours reasonably expended on the litigation by a reasonable hourly rate. Rutherford v. Harris County, Tex., 197 F.3d 173, 192 (5th Cir.1999). The court must then consider whether the lodestar should be adjusted upward or downward, depending on the circumstances of the case and the factors set forth in Johnson v. Georgia Highway Express, Inc., 488 F.2d 714 (5th Cir.1974). A district court must "explain with a reasonable degree of specificity the findings and reasons upon which the award is based, including an indication of how each of the Johnson factors was applied." Von Clark, 916 F.2d at 258.
In this case, the plaintiffs sought an interim award of attorneys' fees, costs and expenses approximating $6.5 million, covering 12,387.9 hours of work performed and nearly a million dollars in out-of-pocket costs. The district court slashed their request and summarily stated that Ms. Demchak's reported hours were "excessive and not necessary" and that the rates she requested were not "usual and customary" for employment discrimination cases in the geographical area. The court offered no reason to deny all compensation for time spent on the lengthy mediation effort; to deny compensation to Mr. Garrigan for his attendance at plaintiff Roald Mark's separate suit against Lufkin; to apply a blanket reduction of 25% to all of the billable hours reported by plaintiffs' counsel; and to reduce the hourly rates requested by plaintiffs' counsel. Because of these deficiencies, we must vacate the fee award and remand for the district court to conduct proper lodestar-fee and Johnson analyses, and award counsel a reasonable reimbursement.

III. CONCLUSION
The district court struggled to complete its work in this wide-ranging, complex discrimination case. Nevertheless, the sum of the foregoing discussion leaves much to be reconsidered. First, we vacate the judgment insofar as it holds Lufkin liable *285 for a claim, unexhausted before the EEOC, that the company discriminatorily assigned newly hired African Americans to the Foundry division. Second, we affirm the judgment of Lufkin's liability to the class for the discriminatory impact of its subjective promotional policies. Because of this split decision, we must vacate and remand the damage award for further proceedings consistent with the foregoing discussion, as well as the award of injunctive relief and attorneys' fees.
AFFIRMED IN PART, REVERSED IN PART, VACATED AND REMANDED IN PART.
NOTES
[1]  Because exhaustion was satisfied, we need not here decide whether exhaustion is a jurisdictional or claim prerequisite. See Pacheco, 448 F.3d at 788 n. 7. See generally Arbaugh v. Y&H Corp., 546 U.S. 500, 126 S.Ct. 1235, 163 L.Ed.2d 1097 (2006) (employee numerosity requirement in 42 U.S.C. § 2000e(b) is an element of a Title VII claim and not a jurisdictional requirement).
[2]  Caselaw also raises considerable doubt that McClain and Thomas would have had standing to assert the class hiring claims of Foundry division workers. See E. Tex. Motor Freight Sys. Inc. v. Rodriguez, 431 U.S. 395, 403, 97 S.Ct. 1891, 52 L.Ed.2d 453 (1977); Vuyanich, 723 F.2d at 1200 (plaintiffs who alleged injury from hiring and termination practices could not represent class arising from other bank employment practices).
[3]  In reviewing the court's findings, we consider evidence adduced during the bench trial but not the class certification hearings. The class certification hearings provided Lufkin limited opportunity for examination on matters going to the merits.
[4]  The testimony of the plaintiffs' expert, Dr. Richard Martell, an Industrial Organization Psychologist, also supports the finding of subjective decision making. Dr. Martell testified that the personnel policies, procedures, and practices at Lufkin were "decidedly subjective." After discussing Lufkin's promotion practices in some detail, Martell ultimately concluded that Lufkin is "awash in a sea of subjectivity that cuts across all manufacturing divisions."
[5]  Specifically, Lufkin argues that the plaintiffs could have used the bid sheets to analyze separately whether blacks bid for jobs at some lesser rate than whites; whether blacks were ineligible for promotion more often than whites because promotion required movement to a higher rated job; whether blacks received fewer promotions because they did not pass a test or declined promotion; whether blacks were disqualified by the requisite minimum qualifications for master classifications or salaried positions more often than whites; and whether Lufkin's practice of promoting only candidates who sign the bid sheets adversely impacts blacks.
[6]  Other courts have reached the same conclusion. See, e.g., Palmer v. Shultz, 815 F.2d 84, 96-97 (D.C.Cir.1987); Coleman v. Exxon Chem. Corp., 162 F.Supp.2d 593, 616 (S.D.Tex.2001).
[7]  Lufkin argues that the court could readily make these determinations by reviewing the bid sheet database. This argument ignores the district court's finding that the bid sheet database was incomplete and unreliable.
[8]  Plaintiffs characterize the district court's decision as a "dismissal" of their disparate-treatment claim; however, the district court clarified that "a disparate treatment claim has not been `dismissed' because a disparate treatment claim was never certified."
