Lead Opinion

COLE, J., delivered the opinion of the court, in which DAUGHTREY, J., joined. CONTIE, J. (pp. 1099-1101), delivered a separate opinion concurring in part and dissenting in part.

*1088OPINION

COLE, Circuit Judge.

The United States appeals the district court’s finding that it failed to establish that the City of Warren’s pre-1986 recruiting practices for municipal positions, other than police and firefighter positions, violated Title VII by having a disparate impact on black potential job applicants. The United States also appeals the district court’s calculation of back pay awarded to Joseph Fears, an unsuccessful job applicant.

The City of Warren cross-appeals, challenging the district court’s finding that Fears is entitled to individual relief based on Fears’s uncorroborated trial testimony and his failure to reapply for a position with the city immediately after it amended its challenged practices. Warren also appeals the district court’s refusal to account for the probability that Fears would not have been hired absent discrimination in calculating his back pay award. For the following reasons, with respect to the United States’ appeal, we REVERSE the district court’s determination and REMAND for further proceedings consistent with this opinion. With respect to the City of Warren’s cross-appeal, we AFFIRM the judgment of the district court.

Warren is located, in Macomb County, Michigan; its southern border abuts the City of Detroit. According to the 1980 census, Warren’s resident civilian labor force included 80,992 people, 0.2% of whom were black. The remainder of Macomb County’s resident civilian labor force of 257,752 people was 1.3% black. The same census indicated that Detroit’s resident civilian labor force of 484,-203 people was 59.7% black.

Prior to October 1986, Warren’s regular recruiting practice was to advertise in three newspapers with circulation primarily in Ma-comb County and to post notices of municipal employment opportunities in municipal buildings. At that time, Warren did not advertise opportunities for municipal work in the Detroit Free Press, the Detroit News, or any other periodicals of general circulation in the Detroit metropolitan area. In addition to these recruiting methods, until 1986, Warren limited its applicant pool by requiring all applicants for municipal positions other than police and firefighter positions to have been Warren residents for a specified duration.1

The history of this lengthy litigation began on February 7,1986, when the United States notified the Warren City Attorney by letter that the Department of Justice planned to investigate claims that “the City of Warren may be engaged in employment practices that discriminate against blacks unlawfully on the basis of race,” including “a requirement that applicants for positions with the City of Warren must be residents of the City at the time of application[.]” JA Vol. Ill at 689. Eight months later, on September 23, 1986, the United States sent a “determination letter,” a document the Department of Justice uses to apprise potential defendants of the results of its investigation. The letter notified the city that the United States’ investigation revealed a pattern or practice of discrimination and that Warren’s recruiting practices and preapplication residency requirements adversely impacted potential black applicants’ employment prospects. After attempts at settlement failed, the United States filed suit against the City of Warren on October 31, 1986, alleging that Warren had violated Title VII of the Civil Rights Act of 1964, as amended, 42 U.S.C. § 2000e et seq., by engaging in a pattern or practice of employment discrimination on the basis of race. The complaint reiterated the findings set forth in the September 23 determination letter, citing the preapplication residency requirement and the city’s recruitment practices as violations of Title VII.

On February 14, 1991, five years after the United States filed its complaint, the district court granted the United States’ renewed *1089motion for partial summary judgment, holding that Warren’s preapplieation residency requirement violated Title VII because it had a disparate impact on black applicants for municipal positions. See United States v. City of Warren, 759 F.Supp. 355, 368 (E.D.Mich.1991) (“City of Warren /”). . The district court found “gross statistical disparities” of 10.3 standard deviations between the number of black employees that the city employed and the expected number of black city employees, basing its findings on the number of black workers in the Detroit metropolitan area civilian labor force and among private employers in Warren, as well as on Warren’s applicant flow data after 1986. See id. at 359-63. In addition, the district court held that Warren could not justify its preapplieation residency requirement for any municipal positions. See id. at 364. The United States, having proved its allegations concerning Warren’s residency requirement, turned its attention to the city’s municipal employment recruiting practices.

In early 1992, the district court held a bench trial on the United States’ contentions that Warren’s recruitment and selection of municipal employees had a disparate impact on blacks, that Warren treated black applicants for employment differently than it treated similarly situated whites, that Warren maintained a racially hostile work environment, and that Warren had failed to correct the effects of its unlawful discriminatory policies and practices. The United States presented evidence that Warren recruited firefighters in March and April 1985 and police officers in January and February 1986 by posting both positions at local universities and colleges and advertising in Macomb County publications. The city advertised neither police nor firefighter job opportunities in any Detroit newspapers. In August 1985, of the 182 people who applied for firefighter positions, none were black, and of the approximately 400 police applicants, only one was black. After October 1986, Warren began advertising its police and firefighter positions in publications outside Macomb County, such as the Detroit News and the Detroit Free Press. This broadened recruitment effort significantly impacted the racial composition of the applicant pool. For example, the 1987 recruitments for police and firefighter positions attracted fifty black applicants as compared to the single black applicant fi*om the previous recruiting season.

In August 1992, the district court ruled that the United States had not met its burden with regard to the disparate treatment, hostile work environment, and post-1986 recruiting claims. See United States v. City of Warren, 1992 WL 509994 (E.D.Mich. August 12, 1992) (“City of Warren II ”). The court also ruled, however, that Warren’s pre-1986 policy of refusing to advertise openings for police officers and firefighters outside of Ma-comb County resulted in unlawful racial discrimination, reasoning that the statistical difference in the number of black applicants for police and firefighter positions before and after 1986, when Warren began advertising police and firefighter employment outside Macomb County, indicated that the advertisement indeed had a disparate impact on black potential employees. See id. at **3-4. The court also noted that Warren failed to offer a business justification for its pre-Octo-ber 1986 recruiting practices. However, City of Warren II limited its finding of disparate impact to police and firefighter positions, holding that the United States had presented no statistical evidence that isolated the discriminatory effect of the recruiting practices on other municipal positions and therefore had not proved that the city’s recruiting practices had a disparate impact on blacks for all municipal positions. See id. at **3-4, *28 n. 4. Lastly, the district court found that because the municipal work force in Warren remained only one percent black as of March 1991, the city had not eradicated the effects of its prior discrimination. See id. at *23. The court therefore enjoined Warren from “failing or refusing to remedy the effects of its pre-October 1986 recruitment practices that have had the effect of unlawfully discriminating on the . basis of race, and from engaging in any future recruitment or selection ... practices that have the purpose or effect of unlawfully discriminating on the basis of race.” JA at 544. Accordingly, the district court’s injunction directed Warren to advertise municipal employment opportunities in newspapers with general circulation in the Detroit metropolitan area; the city therefore expanded its recruiting efforts by *1090advertising in newspapers with a primarily black readership in which Warren previously had refused to advertise.

1. Identification of Victims

The remedial stage of this action proved to be at least as controversial as the litigation. In January 1993, the district court granted the United States’ request to notify victims of' Warren’s past discriminatory practices that they may have been entitled to relief. On June 28,1993, the court entered an order describing the procedure the United States should use to identify victims of Warren’s Title VII violations.2

Out of 300 claims, the United States narrowed the list of possible victims to 75 people. This list shrank to thirty individuals in August 1994 after the court granted Warren’s motion for partial summary judgment to exclude forty-five claimants who stated that they would have applied for positions other than police officer or firefighter positions had they known of the openings, but were unaware of the preapplication residency requirement. The court declined to allow these claims to proceed, reasoning that they were inconsistent-with its prior ruling that the United States had not presented sufficient evidence to prove that Warren’s recruiting practices had a disparate impact on applicants for positions other than police and firefighter positions.

In light of the court’s ruling, the United States re-evaluated the remaining group of thirty claimants and narrowed it further, recommending relief for eleven individuals. Warren moved for summary judgment a second time, asserting that none of the eleven individuals was entitled to relief, and that any relief granted should be' limited by various enumerated factors. In March 1996, the district court granted Warren’s motion with respect to three claimants whom the court found could not prove they would have applied for police or firefighter positions but for the discrimination. Thus, eight individual claimants remained.

2. Back Pay Period

In the same March 1996 decision, the district court held that any victims would be entitled to back pay beginning two years before October 31, 1986, the date the United States filed the complaint.3 The court rejected the United States’ argument that victims were entitled to back pay beginning two years before February 7, 1986, the date the United States sent Warren the letter notifying the city of the pending investigation of its practices, reasoning in part that the United States had not attached a copy of the February 7 letter in its opposition to the summary judgment motion.4 At the same time, the court denied Warren’s motion to exclude overtime pay from any back pay calculations, noting that Title VII’s purpose is to make victims of discrimination whole, including any overtime they would have earned had they been hired absent discrimination.

The United States moved for reconsideration of the beginning date of the back pay period and attached the February 7 letter in question. The district court denied the motion for reconsideration on the grounds that the letter did not provide Warren with enough notice of its unlawful employment *1091practices. The court acknowledged that the letter mentioned the residency requirement, but noted that it did not cite the city’s recruiting practices, and because the case involved both claims, the letter provided insufficient notice.

3. Calculation of Joseph Fears’s Award

In June 1996, the district court held a four-day evidentiary hearing to determine the eligibility of the eight remaining individual claims for relief. On November 6, 1996, the court granted relief to a single claimant, Joseph Fears, finding that he attempted to apply for a position with the Warren Police Department in 1979, but was not allowed to apply because of the city’s preapplication residency requirement. The district court denied relief to the other claimants, finding that they did not or would not have applied for employment during the times that Warren was accepting applications, or that they would not have accepted positions with the city at any rate. The court awarded Fears $55,595 in back pay beginning two years before the United States filed the complaint and ending November 13, 1990, the day Fears was terminated from the Detroit Police Department for misconduct, a date the United States did not contest.

The district court adopted Warren’s proposed calculation of prejudgment interest on Fears’s back pay award.5 The court also reduced Fears’s back pay by an “attrition factor” equal to the percentage of police officers that Warren hired during the time in question, who no longer remained in their positions as of March 1996. Lastly, the district court declined to include as part of Fears’s back pay award any overtime he might have earned as a Warren police officer.6

This timely appeal followed.

II. Disparate Impact Under Title VII

The United States challenges the district court’s finding that it did not establish that Warren’s recruiting practices for all municipal positions had a disparate impact on black potential job applicants in violation of Title VII. We review a district court’s findings of fact for clear error. See Bazemore v. Friday, 478 U.S. 385, 398, 106 S.Ct. 3000, 3008, 92 L.Ed.2d 315 (1986); Scales v. J.C. Bradford and Co., 925 F.2d 901, 907 (6th Cir.1991). In the present case, we believe that the district court clearly erred in finding that the United States failed to establish racial discrimination based on disparate impact in violation of Title VII for municipal positions other than police and firefighter.

The Supreme Court has long held that Title VII of the Civil Rights Act of 1964, 42 U.S.C. § 2000e et seq., proscribes both overt discrimination as well as “practices that are fair in form but discriminatory in operation.” Griggs v. Duke Power Co., 401 U.S. 424, 431, 91 S.Ct. 849, 853, 28 L.Ed.2d 158 (1971). The plaintiffs burden in a Title VII disparate impact case is to prove that a particular employment practice has caused a significant adverse effect on a protected group. See Wards Cove Packing Co. v. Atonio, 490 U.S. 642, 657, 109 S.Ct. 2115, 2125, 104 L.Ed.2d 733 (1989); Scales, 925 F.2d at 908 (citing Watson v. Fort Worth Bank & Trust, 487 U.S. 977, 108 S.Ct. 2777, 101 L.Ed.2d 827 (1988)). Once the plaintiff establishes the adverse effect, the burden shifts to the employer to produce evidence that the *1092challenged practice is a business necessity. See Wards Cove, 490 U.S. at 659, 109 S.Ct. at 2126.

In the present case, the question before the district court was whether the United States met its burden of establishing that the City of Warren’s recruiting practices for municipal positions other than police and firefighter positions resulted in a disparate impact on black job applicants. The district court held that the United States did not meet this burden because it was unable to isolate the challenged recruiting practices as the reason that Warren’s applicant pool for municipal positions, other than police or firefighter positions, included few, if any, blacks before 1986. See City of Warren II, 1992 WL 509994 at *4, *27 n. 4. We believe, however, that the United States’ inability to isolate the specific reason for the dearth of black applicants was not fatal to its claim under these circumstances.

At trial, the United States presented evidence that Warren’s pre-1986 refusal to advertise police and firefighter job openings outside of predominantly-white Macomb County resulted in a practically all-white applicant pool for those positions. See id. at *3. After 1986, when Warren began to advertise municipal employment in periodicals with a circulation in the Detroit metropolitan area, the racial composition of the applicant pool for city jobs changed dramatically, and the number of black applicants increased by six standard deviations.7 See id. at *4. In holding that Warren’s recruiting methods violated Title VII, the district court noted that “as a general rule, a statistical disparity of more than two to three standard deviations may properly ... support an inference of discrimination.” Id. (citing Hazelwood Sch. Dist. v. United States, 433 U.S. 299, 311 n. 17, 97 S.Ct. 2736, 2744 n. 17, 53 L.Ed.2d 768 (1977)). The district court also cited the absence of statistical data for the recruitment of municipal employees other than police or firefighters which would demonstrate that the recruitment for municipal positions generally had a disparate impact on blacks. See City of Warren II, 1992 WL 509994 at *4.

The United States contends that it did not produce statistical analyses of the impact of Warren’s refusal to advertise municipal positions other than police or firefighter positions outside Macomb County before 1986, because the city’s advertising policies combined with its preapplication residency requirement for all municipal employees until 1986 rendered such an analysis meaningless. The district court had held that Warren’s pre-1986 residency requirement for all municipal positions was unlawful. See City of Warren I, 759 F.Supp. at 368. Therefore, until 1986, both the residency requirement and the advertising policies circumscribed Warren’s municipal employment applicant pool. Because of this confluence of factors, the United States asserts that a comparison of the pre- and post-1986 recruitment for municipal positions other than police and firefighter positions would not isolate whether the residency requirement, the recruitment practices, or both were responsible for the absence of black applicants for Warren city employment. See City of Warren II, 1992 WL 509994 at *27 n. 4.

The district court interpreted the absence of specific statistical evidence demonstrating the impact of Warren’s pre-1986 recruitment practices for non-police and non-firefighter positions on black applicants to mean that the United States had not met its burden of production. See City of Warren II, 1992 WL 509994 at *4. However, in earlier incarnations of the same litigation, the district court had already determined the particular sources of the alleged Title VII violations. In City of Warren II, the court acknowledged that Warren’s recruiting practices for police and firefighter positions had a disparate impact on black potential employees in violation of Title VII. See id. The court also noted that the city’s recruiting methods were substantially the same for all municipal job opportunities, police, fire and others. See id. *1093at *3 (“Prior to October 1986, Warren’s general recruitment practice for municipal jobs was not to [advertise] in the ... newspapers of general circulation in the Detroit metropolitan area.”). Six years prior, the district court held that Warren violated Title VII by maintaining a preapplieation residency requirement for municipal employment before 1986.8 See City of Warren I, 759 F.Supp. at 368. Therefore, according to the district court’s own reasoning, Warren’s pre-1986 employment practices for non-police and non-firefighter municipal positions violated Title VII for two reasons: the residency requirement and the challenged recruiting practices. Hence, the court’s limitation of its finding that Warren’s recruitment methods violated Title VII only as to police and firefighter recruitment is inconsistent with its own findings of fact and prior holdings in this case. See generally Wright, Miller «fe Cooper, Federal Practice and Procedure: Jurisdiction § 4478 -(1981) (explaining that “[l]aw of the case rules have developed to maintain consistency and avoid reconsideration of matters once decided during the' course of a single continuing lawsuit”). Accordingly, we conclude that the district court’s finding that the United States did not meet its burden of establishing the disparate impact of Warren’s recruitment practices with regard to all municipal positions, was clearly erroneous.

In response to the district court’s finding that the United States lacked statistical evidence of the disparate impact of non-police and non-firefighter municipal positions, both the United States and the City of Warren rely on the Supreme Court’s analysis in Wards Cove Packing v. Atonio, 490 U.S. at 650, 657, 109 S.Ct. at 2121, 2125. Warren contends that Wards Coverequires the United States to identify the specific employment practice it challenges and offer statistical evidence demonstrating that the challenged practice has had a disparate impact on members of a protected class. Warren is correct that Wards Cove generally requires a plaintiff to meet this two-step burden. 490 U.S. at 657, 109 S.Ct. at 2125. However, Wards Coveexplicitly relaxes this requirement in cases in which such “labor market statistics -will be difficult if not impossible to ascertain.” Id. at 650,109 S.Ct. at 2121. In those instances, “measures indicating the racial eomposition of ‘otherwise-qualified applicants’ for at-issue jobs are equally probative,” and “where ‘figures for the general population might ... accurately reflect the pool of qualified job applicants,’” Wards Cove recognizes that plaintiffs may “rest their prima facie cases on such statistics as well.” Wards Cove, 490 U.S. at 651, 109 S.Ct. at 2121 (citing New York City Transit Authority v. Beazer, 440 U.S. 568, 585, 99 S.Ct. 1355, 1365, 59 L.Ed.2d 587 (1979)); see also Wards Cove, 490 U.S. at 651, n. 6, 109 S.Ct. at 2121, n. 6 (citing Teamsters v. United States, 431 U.S. 324, 340, n. 20, 97 S.Ct. 1843, 1857, n. 20, 52 L.Ed.2d 396 (1977)).

Because of the concurrence of the residency requirement and the challenged recruiting practices, the statistical proof which Wards Cove generally requires was unattainable in this case. However, as noted above, Wards Cove allows plaintiffs to provide alternative statistics under these circumstances. Here, the United States presented statistical evidence reflecting the racial composition of the population from which Warren would have recruited its workers absent discrimination; in addition, the United States offered data comparing the number of black applicants before and after Warren’s expanded recruiting campaign. See City of Warren II, 1992 WL 509994 at **3-4. The district court found that this analysis established that Warren’s recruitment practices for police and firefighter positions violated Title VII. Because the recruitment practices for all municipal positions were identical, we hold that the district court clearly erred in holding that the United States did not meet its burden with regard to municipal positions other than police and firefighter positions. The district court granted summary judgment in favor of the United States, finding that the city’s preapplieation residency requirement had a disparate impact on black. potential applicants; therefore, the United States clearly met its burden with regard to *1094that charge. See City of Warren I, 759 F.Supp. at 368.

Wards Cove does not preclude the United States’ claim for failing to isolate and quantify the effects of Warren’s discriminatory employment practices simply because two practices, both of which the district court has held to be unlawful, converged to discourage black applicants. Indeed, such a result would be anomalous and contrary to Wards Cove’s explicit recognition that when, as here, certain employment practices obscure labor-market statistics, alternative statistical analysis suffices to establish a prima facie disparate impact case. See Wards Cove, 490 U-S. at 651 n. 6, 109 S.Ct. at 2121 n. 6. The United States has met its burden by proving that Warren’s proffered advertising methods resulted in a statistical disparity. Plaintiffs who present a statistical analysis of some challenged practice need not rule out all other variables to prevail. See Scales, 925 F.2d at 908-09 (citing Bazemore v. Friday, 478 U.S. at 400,106 S.Ct. at 3009) .(“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.”). This principle is particularly applicable where “the evidence actually presented on its face conspicuously demonstrates ... grossly discriminatory impact.” Dothard v. Rawlinson, 433 U.S. 321, 331, 97 S.Ct. 2720, 2727, 53 L.Ed.2d 786 (1977). The fact that as of 1986, when both the durational residency requirement and the challenged recruiting practices were intact, the City of Warren employed not a single black person out of a workforce of 1500 certainly demonstrates a grossly discriminatory impact.' Statistical analysis is unnecessary to establish this point.9 City of Warren I, 759 F.Supp. at 360-63.' Quite simply, the City of Warren should not escape liability because it maintained two discriminatory practices which acted concurrently to exclude black applicants. See United States v. Town of Cicero, 786 F.2d 331, 336 (7th Cir.1986) (Posner, J., concurring and dissenting) (“[I]t is no defense to a discriminatory practice that it merely backs up other forms of discrimination.”).

Moreover, Warren’s assertion that disparate impact analysis is inapplicable to its recruiting practices is plainly incorrect.10 The very purpose of Title VII’s disparate impact theory is to “eradicat[e] ... barriers which discriminate on the basis of race, gender, religion, and other protected classifications.” Zamlen v. City of Cleveland, 906 F.2d 209, 216 (6th Cir.1990) (citing Griggs, 401 U.S. at 424, 91 S.Ct. at 849). Warren’s limitation of its applicant pool to residents of the overwhelmingly white city, combined with its refusal to publicize jobs outside the racially homogeneous county, produced a de facto barrier between employment opportunities and members of a protected class. A plaintiff need not identify a sign reading “No Blacks Need Apply” before invoking Title VII. The disparate impact theory subjects any facially neutral policy with a discriminatory effect to Title VII. See Zamlen, 906 F.2d at 216 (citing Wards Cove Packing, 490 U.S. at 642, 109 S.Ct. at 2115).

For the foregoing reasons, we hold that the district court was clearly erroneous in finding that the United States did not establish that Warren’s recruiting practices for all municipal positions had a disparate impact on black potential job applicants in violation of Title VII. Therefore, we reverse the district court’s holding on this issue.

III. Calculation of Relief

A. Commencement of Back Pay Period

We review a district court’s designation of the beginning of a back pay period for an abuse of discretion. See EEOC v. Wilson Metal Casket Co., 24 F.3d 836, 840 *1095(6th Cir.1994). “Abuse of discretion is defined as a definite and firm conviction that the trial court committed a clear error of judgment.” Logan v. Dayton Hudson Corporation, 865 F.2d 789, 790 (6th Cir.1989). In its March 1996 decision, the district court determined that the back pay compensation would begin to accrue for all claimants in this case as of October 31,1984, two years before the United States filed its complaint. The United States contends that its letter of February 7, 1986, informing Warren that it would investigate the city’s employment practices, provided the city with sufficient notice such that the back pay period should begin on February 7, 1984. The district court declined to use the February 7 letter to measure the beginning of back pay accrual because the United States had not provided the court with the contents of the letter. However, when the district court was provided with the letter, it concluded that it was insufficient to provide Warren notice of its questionable practices in order for back pay to begin to accrue February 7,1984.

Section 706(g) of Title VII as amended in 1972 provides that “[b]ack pay liability shall not accrue from a date more than two years prior to the filing of a charge with the [Equal Employment Opportunity] Commission.” 42 U.S.C. § 2000e-5(g). See, e.g., Winbush v. State of Iowa by Glenwood State Hosp., 66 F.3d 1471, 1477 n. 8 (8th Cir.1995); Bereda v. Pickering Creek Indus. Park, Inc., 865 F.2d 49, 54 (3d Cir.1989). However, Title VII is silent as to how the two-year back pay provision of Section 706(g) applies to civil rights suits that are brought by the Attorney General under her authority to bring pattern or practice suits under Section 707(a), 42 U.S.C. § 2000e-6(a). In Wilson Metal Casket Co., we noted that the purpose of Title VII’s requirement that claimants file charges with the EEOC is to “give notice of potential Title VII liability to an alleged wrongdoer and allow the EEOC to attempt to conciliate with the wrongdoer rather than go to court.” 24 F.3d at 839 (citation omitted). To this end, in a pattern or practice case, the back pay period should begin whenever the United States provides the employer with notice and information comparable to that normally contained in a charge of discrimination filed with the EEOC.11

The narrower question before us, then, is whether the district court abused its discretion in finding that the United States’ letter of February 7, 1986 did not identify sufficiently the “relevant facts of the alleged discrimination”' such that it could substitute for a complaint filed with the EEOC. We believe that the February 7 letter failed to provide such notice. The much-disputed letter stated in relevant part that the United States had received information indicating that the' City of Warren may have been conducting employment practices which discriminated against blacks unlawfully on the basis of race; the letter cited the residency requirement and indicated that the United States would investigate in order to gamer additional information. The letter did not mention the city’s recruiting practices, which have since become a central issue in this case. More significantly, the letter served more to inform Warren of the pending investigation than to give the city notice that specific practices were in violation of Title VII. Therefore, we hold that the district court did not abuse its discretion in. refusing to accrue back pay beginning February 7,1984.

The United States, however, sent Warren a determination letter dated September 23, 1986, identifying both the recruiting practices and the residency requirement as violating Title VII. The determination letter provides the city with ample notice of the claims against it and of its challenged practices. Therefore, it would appear that Fears’s back pay should accrue beginning September 23, 1984. Thus, we believe that the district court abused its discretion by failing to consider that date. We therefore remand this issue for the district court to determine whether Fears’s back pay should accrue beginning September 23, 1984. In addition, we note that the date ultimately determined by the district court would apply to back pay relief for any claimants previously excluded by the district court’s erroneous *1096holding in City of Warren II, discussed in Part II, above.

B. Calculation of Prejudgment Interest

We review the trial court’s calculation of prejudgment interest for an abuse of discretion. See Thurman v. Yellow Freight Systems, Inc., 90 F.3d 1160, 1170 (6th Cir.1996).- “A court abuses its discretion when it relies on clearly erroneous findings of fact, or when it improperly applies the law or uses an erroneous legal standard.” Phelan v. Bell, 8 F.3d 369, 372 (6th Cir.1993) (quoting Christian Schmidt Brewing Co. v. G. Heileman Brewing Co., 753 F.2d 1354, 1356 (6th Cir.1985)). The award or denial of prejudgment interest is within the sound discretion of the trial judge. See Scales, 925 F.2d at 908 (citation omitted).

Prejudgment interest is usually appropriate to make a discrimination plaintiff whole. An award of prejudgment interest “is an element of complete compensation” in a Title VII back pay award. Thurman, 90 F.3d at 1170 (citing Wilson Metal Casket, 24 F.3d at 841-42) (Prejudgment interest “helps to make victims of discrimination whole and compensates them for the true cost of money damages they incurred.”). We commonly award prejudgment interest on back pay awards. See Wilson Metal Casket, 24 F.3d at 841-42. Moreover, victims of discrimination should not be penalized for delays in the judicial process, and discriminating employers should not benefit from such delays. See Thurman, 90 F.3d at 1170 (citing Wilson Metal Casket, 24 F.3d at 842). The purpose of awarding prejudgment interest under Title VII, however, is to compensate victims both for the time value of the lost money as well as for the effects of inflation. See EEOC v. O’Grady, 857 F.2d 383, 392 (7th Cir.1988).

The district court awarded one claimant, Joseph Fears, prejudgment interest on his back pay award. In calculating that interest, the court equated the interest rate with the consumer price index (“CPI”), in accordance with the opinion of the City of Warren’s expert witness. The United States contends that the district court abused its discretion in its calculation of Fears’s interest, primarily because the consumer price index does not compensate victims for the time value of the lost money; rather, the CPI simply ensures that inflation does not erode the value of money.

Although we generally afford the district court great discretion in the calculation of prejudgment interest, no authority in the courts of appeals or in the Supreme Court supports the use of the CPI as a substitute for a market interest rate, and the circuit courts that have ruled on this issue explicitly hold that the CPI is not an adequate basis for prejudgment interest. Both the Second Circuit and the D.C. Circuit have held that merely adjusting the dollars the plaintiff would have earned to compensate for diminished purchasing power because of inflation does not compensate for the lost use of the money in the intervening time. See Chandler v. Bombardier Capital, Inc., 44 F.3d 80, 84 (2d Cir.1994); Clinchfield Coal Co. v. Federal Mine Safely and Health Review Comm’n, 895 F.2d 773, 780 (D.C.Cir.1990) (Interest rates based on the CPI award claimants “compensation for losses through inflation but none for the capacity of wealth to generate more wealth (and lenders’ insistence on corresponding compensation), which a market interest rate reflects.”).

The lack of authority supporting the district court’s use of the CPI, coupled with the failure of the CPI to make victims of discrimination whole according to the purposes of Title VII, clearly establish that the trial court improperly applied the law by using an erroneous legal standard. Therefore we find that the district court abused its discretion.12 See Phelan, 8 F.3d at 372. Accordingly, we remand the issue of prejudgment interest to the district court to determine an appropriate interest rate for Fears’s award.

C. Back Pay Calculation: Overtime Compensation and Attrition Factor

The United States appeals the district court’s refusal to include overtime as *1097part of Joseph Fears’s back pay award. We review a district court’s calculation of back pay and its decision not to award back pay for abuse of discretion. See Wilson Metal Casket, 24 F.3d at 840. A victim of discrimination “is to be placed, as near as may be, in the situation he would have occupied if the wrong had not been committed.” Albemarle Paper Co. v. Moody, 422 U.S. 405, 418-19, 95 S.Ct. 2362, 2372, 45 L.Ed.2d 280 (1975). Moreover, we have acknowledged that lost overtime pay “should be included in back pay,” Meadows v. Ford Motor Co., 510 F.2d 939, 947 (6th Cir.1975), and a district court must ensure that back pay awards “completely redress the economic injury the claimant has suffered as a result of the discrimination.” Rasimas v. Michigan Dep’t of Mental Health, 714 F.2d 614, 626 (6th Cir. 1983). In excluding overtime compensation from Fears’s back pay compensation, the district court relied on the testimony of former Warren police commissioner Paul Pash who stated that officers in police departments other than Warren’s would not have earned the same amount of overtime as Warren police officers with whom they were compared, unless they had previously held jobs with similar functions as those “performed by the comparable Warren officers.”. However, the district court did not address the city’s calculations showing that the people it hired as police officers at the time Fears would have been hired earned between $12,000 and $35,000 in overtime. Rather, the district court declined to award Fears overtime on the theory that it would provide a “windfall” by compensating him for “work he did not perform.”

Because lost overtime is a well-established part of a back pay award under Title VII, the district court’s reasoning that including overtime in Fears’s award would be a “windfall” is inconsistent with that court’s finding that Warren would have hired Fears but for discrimination. The district court’s exclusion of back pay from Fears’s award does not place him as near as possible to the position he would have occupied absent discrimination. Therefore, the district court did not apply the law properly, and we find that it abused its discretion with regard to this issue. However, this court is not a fact-finding court. Therefore, we remand the overtime issue to the district court to determine whether all police officers whom Warren hired during the time Fears applied earned overtime and whether Fears’s position with the Detroit Police Department was comparable to that of Warren police officers who earned overtime.

The United States also appeals the district court’s application of an “attrition factor” to Fears’s back pay calculation. The district court provided no discernible reason for its application of the attrition factor. However, the attrition of police officers from the Warren Police Department was- not an appropriate factor to consider in this case because the district court had already terminated Fears’s back pay as of November 1990, the date that he left the Detroit Police Department. The court’s limitation of Fears’s back pay by both the time that he actually stopped working and the time that similarly situated Warren police officers left their jobs amounts to double-counting, an improper application of the law and therefore an abuse of discretion. Accordingly, we remand this issue, and note that in calculating Fears’s back pay award, the district court should apply either the actual date that Fears stopped working, or the attrition factor, keeping in mind that “ambiguity in what the claimant would have received but for the discrimination should be resolved against the discriminating employer.” Rasimas, 714 F.2d at 628; see also Wooldridge v. Marlene Industries Corp., 875 F.2d 540, 549 (6th Cir.1989) (“[G]uidelines for back pay awards under Title VII have effectively shifted the risk of error in favor of the back pay claimant.”).

IV. City of Warren’s Cross Appeal

A. Award of Back Pay to Joseph Fears

In its cross-appeal, the City of Warren challenges the award of back pay to Joseph Fears. We review a district court’s' award and calculation of relief for abuse of discretion. See Wilson Metal Casket Co., 24 F.3d at 840.

B. Joseph Fears’s Trial Testimony

The City of Warren contends that the district court abused its discretion in *1098awarding Joseph Fears back pay “based solely on Fears’[s] uncorroborated, self-serving testimony.” The City of Warren essentially asks us to review the credibility of Joseph Fears as a trial witness and assess the weight the trial judge accorded to Fears’s testimony. We “may neither weigh the evidence [nor] pass on the credibility of witnesses ...” Ratliff v. Wellington Exempted Village Schools Bd. of Educ., 820 F.2d 792, 795 (6th Cir.1987); see also Anderson v. City of Bessemer City, 470 U.S. 564, 573, 105 S.Ct. 1504, 1511, 84 L.Ed.2d 518 (1985) (Due regard is given to opportunity of trial court to judge credibility of witnesses.). Therefore, we decline to disturb the district court’s assessment of Fears’s credibility and conclude that the court did not abuse its discretion by awarding Fears back pay.

C. Fears’s alleged failure to mitigate damages

In the alternative, Warren argues that the district court abused its discretion in awarding Fears back pay despite his alleged failure to mitigate damages by waiting to reapply for a position with the city until 1991, seven years after Warren eliminated the residency requirement for police applicants. In an apparent case of first impression, Warren asks us to consider whether a Title VII claimant who was never hired because of discriminatory employment practices is precluded from a back pay award because he did not reapply for work with the same employer when it eliminated its discriminatory practices. The district court found that Fears’s failure to reapply to the City of Warren did not equal a failure to mitigate damages, and therefore, did not preclude his back pay award. We affirm the district court’s decision.

A Title VII claimant has a duty to mitigate damages by seeking substantially equivalent employment. See Ford Motor Co. v. EEOC, 458 U.S. 219, 231-32, 102 S.Ct. 3057, 3065-66, 73 L.Ed.2d 721 (1982). “This duty has ancient origins, and operates to prevent claimants from recovering for damages which they could have avoided through reasonable diligence.”. Rasimas, 714 F.2d at 623. In this case, Fears worked as an officer with the Detroit Police Department from July 1985 to November 1990. He therefore found and pursued employment comparable to that he would have enjoyed with the City of Warren absent discrimination. Thus, Fears’s work as a Detroit police officer satisfies Title VII’s requirement that he mitigate his damages.

Warren asks us to reach the inequitable conclusion that Fears should have been aware of the City’s elimination of its residency requirement for police applicants in 1984 and he was therefore obligated to reapply to the Warren police force after he had been working in Detroit.' We decline to reach this result. No established authority requires Title VII claimants who have found comparable employment to reapply for positions with employers who have previously refused to hire them for discriminatory reasons. This is simply not a hoop Title VII requires claimants to jump through, and we will not be the first to require it.

For the above stated reasons, we find that the district court did not abuse its discretion in awarding Joseph Fears back pay, and we affirm this aspect of the district court’s opinion.13

D. The “Probability of Hire” Factor

Warren asks us to review the district court’s refusal to reduce Fears’s back pay award by a factor which represents the probability that the city would have hired him absent discrimination. The district court recognized Warren’s argument that without the residency requirement more qualified applicants would have applied for police positions, and therefore, Fears’s likelihood of being hired would have been less than 100%. However, the court noted that the information before it was insufficient to *1099allow a determination representing which percentage would appropriately reflect the “probability of hire.” The district court correctly applied the principle that “[ajmbiguity should be resolved ‘against the discriminating employer’ and when ‘it is impossible to reconstruct the employment of each claimant, back pay equal to the maximum amount which could have been earned but for the discrimination is appropriate.’” JA at 108.

The cases the City of Warren cites, Ingram v. Madison Square Garden Center, Inc., 709 F.2d 807, 812 (2d Cir.1983), and Dougherty v. Barry, 869 F.2d 605, 615 (D.C.Cir.1989), are distinguishable from the present case in that they involved several" victims of discrimination whose numbers exceeded the number of available positions. In this case, neither party disputes that Warren hired twenty-four of the twenty-five applicants for police jobs during the time that Fears would have applied, and by all accounts Fears was qualified for such a position, as evidenced by his securing employment with the Detroit Police Department within the same time frame. Therefore, the district court was correct in resolving the attendant ambiguity in favor of Fears; the victim of discrimination in this case.

Accordingly, we affirm the district court’s decision not to reduce Fears’s back "pay by the undetermined “probability of hire” factor.

For the foregoing reasons, we REVERSE the district court’s finding that the United States did not establish that the City of Warren’s recruiting practices had a disparaté impact on black applicants for all municipal positions and REMAND for further proceedings consistent with this opinion.

We also REMAND to the district court for a determination consistent with this opinion the following issues:

(1) the date of accrual of back pay for Joseph Fears or any other successful claimant; , .,

(2) the appropriate market rate for prejudgment interest;

(3) the inclusion of overtime in Fears’s. back pay award;

(4)the calculation of Fears’s back pay award, applying either the attrition factor or the date Fears stopped working.

With respect to the City of Warren’s cross appeal, we AFFIRM the district court’s judgment that Joseph Fears was entitled to individual relief and AFFIRM the district court’s decision not to use the “probability of hire” factor in calculating Fears’s báck pay.

Notes

. In 1984, Warren eliminated its residency requirement for police and firefighters after a Michigan court of appeals held that requiring residency for those positions violated applicants' constitutional right to travel. See Musto v. Redford Township, 137 Mich.App. 30, 357 N.W.2d 791 (1984). However, Warren maintained its residency requirement for all other municipal positions until 1986, when a county court invalidated that requirement on constitutional grounds. See Masters v. Warren, No. 86-500-CK (Cir.Ct.Mich. March 28, 1986).

.The order limited the pool of eligible claimants to:

(1) all qualified black individuals who sought employment with Warren between March 24, 1972 (the date the municipalities became subject to Title VII), and May 13, 1986, but who were denied employment because of Warren’s former preapplication residency requirements;

(2) all qualified black individuals who would have applied for employment with Warren between March 24, 1972 and May 13, 1986, but who did not apply to Warren for employment because of residency requirements; and

(3) all qualified black individuals who would have applied for police or firefighter positions with Warren between March 24, 1972 and October 31, 1986, but for Warren's discriminatory recruitment practices.

In all instances the order gave Warren the opportunity to prove that such individuals would have been denied employment for a lawful reason.

. Title VII provides that back pay awards begin to accrue two years prior to the filing of a charge with the EEOC. 42 U.S.C. § 2000e-5(g).

. There was no dispute that the United States had sent the letter, and the letter was part of the case record. .

. The district court adopted the interest rate which Warren’s statistical expert, David Peterson, a Ph.D. in electrical engineering, recommended. Dr. Peterson asserted that prejudgment interest should reflect only inflation and thus equated the interest rate with the consumer-price index.

. In refusing to include overtime in its back pay calculation, the district court relied on the testimony of Warren’s former police commissioner that indicated that a claimant with experience in another police force would not have earned the same overtime as Warren police officers with whom he was compared, unless that claimant had worked in a position with a similar job function as that of a Warren police officer. The court also reasoned that to include overtime in Fears’s back pay would be to award damages for work which he did not perform. This reasoning appears to contradict the court’s decision to award Fears back pay in the first instance, as Title VII's back pay damages, by definition, compensate claimants for work they did not perform; it is also inconsistent with the district court's earlier denial of Warren’s motion to exclude overtime pay.

. In its post-trial brief Warren admitted that its expanded recruiting efforts increased the number of black applicants by ten percent; this statistical data indicated that the city’s recruiting practices indeed had a disparate impact on black potential employees in the labor pool. (“The results the City of Warren has achieved demonstrate the effectiveness of its program ... Overall, since [Warren expanded its recruiting efforts to include media with a black audience], the City has generated 10.2% black applicant flow.").

. As previously stated, a Michigan county court invalidated the residency requirement in 1986 on constitutional grounds; the decision did not implicate Title VII. Masters v. Warren, No. 86-500-CK (Cir.Ct.Mich. March 28, 1986).

. In City of Warren I, the district court acknowledged that the expected number of black municipal employees in Warren in 1986 was ninety-nine. See 759 F.Supp. at 361.

. Relying on this court's holding in Muzquiz v. W.A. Foote Memorial Hosp., Inc., 70 F.3d 422 (6th Cir.1995), Warren proffers that "[t]he group disadvantaged by the City's Macomb County-oriented recruiting was composed of job seekers, black and white, who did not read Macomb County newspapers ...” City of Warren's Brief at 23. Muzquiz is inapposite in this case as its holding impacted physicians trained in Mexico, an unprotected class under Title VII. In the case before us, the challenged practices resulted in discrimination against African Americans, a class clearly protected by Title VII.

. EEOC regulations require simply that a charge of discrimination be in writing, contain the name of the respondent and the relevant facts of the alleged discrimination. See 29 C.F.R. §§ 1601.11, 1601.12(a).

. In addition, we find convincing the United States’ argument that according to the district court’s view, if there were no inflation, plaintiffs would receive no prejudgment interest, regardless of the amount of time they were denied the use of their money and the time the discriminating employer had the use of that same money.

. Generally, on appeal the mitigation of damages is an issue of fact subject to the clearly erroneous standard of review. See Rasimas, 714 F.2d at 623. However, in this case, we are not examining the factual circumstances of Fears’s mitigation. Rather, we are determining whether the district court should have awarded back pay despite Fears’s delay in reapplying for the position. As stated above, the award and calculation of back pay is subject to review for an abuse of discretion. See Wilson Metal Casket Co., 24 F.3d at 840.

Concurrence in Part

CONTIE, Circuit Judge,

concurring in part and dissenting in part.

I respectfully concur in part and dissent in part from the majority’s opinion for the following reasons.

Following years of exhaustive discovery, the district court granted the United States’ motion for .partial summary judgment on February 14, 1991, finding that the city of Warren’s preapplication residency requirement unlawfully prevented many black applicants from seeking positions with the city. Following a bench trial, the district court subsequently found that the city’s recruitment practices failed to inform potential black applicants of job opportunities with the city. The district court, however, limited its disparate impact finding to police officers and firefighters because the city’s discriminatory recruiting practices’ effect on black applicants for all other municipal positions with the city of Warren could not be isolated and determined with any degree of accuracy. In an effort to remedy the disparate impact, the district court ordered the city to improve its recruitment practices by advertising in minority-targeted publications.

On appeal, the United States challenges the district court’s finding that the city of Warren’s pre-1986 recruiting practices did not discriminate against black job applicants seeking employment with the city. Because my colleagues believe that the city of Warren’s actions were racially discriminatory based on a disparate impact analysis, the majority reverses the district court’s decision and remands this action to the district court with instructions to find potential black applicants that were discriminated against by the city of Warren when the city sought to fill all municipal vacancies during the relevant time period. I am of the opinion that the majority *1100did not review the determination of the district court pursuant to the proper standard. The review of the district court’s decision is not de novo. The standard of review is clearly erroneous. If the findings of the district court are not clearly erroneous, we must affirm. Because I steadfastly believe that the district court’s findings are not clearly erroneous, I respectfully dissent from the majority’s decision with respect to the city’s pre-1986 recruiting practices when it sought to fill non-police officer and non-firefighter vacancies with the city.

Once a Title VII plaintiff establishes that a particular employment practice has caused a significant adverse effect on a protected group, the burden shifts to the, employer to prove that the challenged practice is a business necessity. Wards Cove Packing Co. v. Atonio, 490 U.S. 642, 659, 109 S.Ct. 2115, 2126, 104 L.Ed.2d 738 (1989). Though my colleagues believe that the United States met its burden of establishing Warren’s discriminatory practices and the resulting disparate impact on potential black job applicants, I steadfastly believe that the district court’s findings were not clearly erroneous. Simply stated, the United States failed to meet it burden of establishing that the city of Warren’s recruiting practices for municipal positions (other than police and firefighter positions) discriminated against potential black job applicants because the United States did not isolate the reasons why Warren’s applicant pool included few black candidates before 1986.

Indeed, the statistical evidence in this action simply noted the disparity in the number of black individuals that were employed by the city of Warren as policemen and firefighters during the period when the city’s actions were deemed discriminatory. Because the Supreme Court has rejected rigid mathematical formulas in analyzing statistics purporting to show a disparate impact, Watson v. Fort Worth Bank & Trust, 487 U.S. 977, 994-95, 108 S.Ct. 2777, 2788-89, 101 L.Ed.2d 827 (1988), “[cjourts are left to decide on a case-by-case basis whether statistics that purport to show disparate impact are in fact sufficient to the task.” Abbott v. Federal Forge, Inc., 912 F.2d 867, 873 (6th Cir.1990). In this action, the statistics presented by the United States do not support its claim that the city of Warren discriminated in the hiring of all city employees; instead, the statistics support the United States’ claim with respect to police officers and firefighters only. Accordingly, the district court properly limited the unlawful recruiting claims to qualified black individuals who applied, or would have applied, to the city for police officer or firefighter positions only. In other words, though the United States presented statistical evidence reflecting the racial composition of the potential workforce absent discrimination, and though the United States offered data comparing the number of black applicants both before and after Warren’s expanded recruiting practices, the district court properly held that the United States faded to meet its burden with respect to all municipal positions because the data pertaining to Warren’s hiring of police officers and firefighters cannot be extended with any degree of accuracy to Warren’s remaining municipal vacancies.

With respect to Joseph Fears’ claim, I agree with the majority’s finding that Fears is entitled to relief but dispute my colleagues’ back pay determinations because, I believe, the district court did not abuse its discretion when calculating Fears’ back pay award.

The record reveals that more than 300 individuals claimed that they were victims of Warren’s discriminatory practices. After reviewing the claims, the United States recommended relief for 75 claimants. On August 19,1994, the district court narrowed the field of claimants to 30 because the other claimants were not interested in police officer or firefighter positions and were not aware of Warren’s preapplication residency requirement. The United States subsequently dismissed 19 of the 30 claimants that remained. The district court later rejected three of the eleven claimants that remained because the claimants could not prove that, but for the discrimination, they would have applied for positions with the city.

Following an evidentiary hearing, the district court granted relief to only one of the eight remaining claimants, Joseph Fears. The record reveals that Fears sought a position with the Warren Police Department in 1979 but was denied the position because of *1101the city’s preapplication residency requirement. Accordingly, the district court awarded Fears $55,595 in back pay after finding that: Fears’ back pay period began on October 31, 1984 (two years before the United States filed its complaint); Fears’ prejudgment interest should be calculated using the consumer price index as the relevant, interest rate; Fears’ back pay. should be reduced by an “attrition factor” (12.5 percent) to reflect the likelihood that Fears, if hired, would no longer be employed as a Warren police officer; and Fears was not entitled to overtime pay.

Though the goal of Title VII is to “make persons whole for injuries suffered on account of unlawful employment discrimination,” Albemarle Paper Co. v. Moody, 422 U.S. 405, 418, 95 S.Ct. 2362, 2372, 45 L.Ed.2d 280 (1975), Title VII relief must be reasonable. See generally Griffin v. Michigan Dep’t of Corrections, 5 F.3d 186, 189 (6th Cir.1993) (The purpose of Title VII relief “is to put an injured party in the same position the party would have occupied in the absence of the discrimination, neither more nor less.”).

On appeal, the United States asserts that Fears’ back pay period should have begun on February 7,1984, two years before the United States wrote to the city of Warren that it would be investigating charges that the city was engaged in discriminatory employment practices. In response, the city of Warren asserts that the district court properly determined that Fears’ back pay period should commence on October 31, 1984, two years before the United States filed its complaint in district court. I believe that the district court properly found that Fears’ back pay period began on October 31, 1984, because the United States’ February 1986 letter did not mention the unlawful recruiting policies later alleged by the United States. Because the district court did not abuse it discretion by finding that Fears’ back pay period began on October 31, 1984, I respectfully dissent from that portion of the majority’s opinion.

The district court used the consumer price index as the “rate of interest” when ealeulat-ing Fears’ back pay award (which resulted in an average rate of slightly more than four percent). On appeal, the United States asserts that the district court erred because it did not explain its reasoning for using the consumer price index as the relevant interest rate. In response, the city of Warren asserts that the United States failed to show that the. district court abused its discretion by awarding prejudgment interest tied to the consumer price index. The district court’s decision whether to grant prejudgment interest, and the interest rate to be used, must not be overturned on appeal absent an abuse of discretion. EEOC v. Wilson Metal Casket Co., 24 F.3d 836, 841 (6th Cir.1994). Though the United States may prefer that a higher interest rate be used, the district court did not abuse its discretion by using the familiar and often-cited consumer price index as the relevant interest rate. • Accordingly, the district court properly calculated the prejudgment interest to be awarded to Fears.

To the extent that the district court re^ duced Fears’ back pay by an attrition factor reflecting the percentage of Warren police officers that were no longer employed by the city at the time of Fears’ evidentiary hearing, the city of Warren properly asserts that the district court’s reduction of Fears’ back pay award by the attrition factor (12.5%) accurately reflects the likelihood of Fears’ continued employment with the city absent Warren’s discriminatory practices. Though the use of an attrition factor is necessarily imprecise because it is impossible to determine with certainty how long Fears would have been employed by the city, the district court did not abuse its discretion by reducing Fears’ back pay award by 12.5 percent to reflect the likelihood that Fears, if hired by the city in 1979, would, still be employed as a Warren police officer. Accordingly, I believe that the district court did not abuse its discretion by using an attrition factor to reduce Fears’ back pay award.

Because I would affirm the district court’s determinations in their entirety, I concur in part and dissent in part from the majority’s opinion.