SEYMOUR, Circuit Judge.

Janice Pitre brought this suit individually and on behalf of a class of similarly situated employees under 42 U.S.C. § 2000e et seq. (1988) (Title VII) against Western Electric Co., Inc., asserting that the company had engaged in a continuing practice of sex discrimination with respect to promotions and downgrades of its salaried employees. The district court found the company liable and awarded Pitre and the class back pay, front pay, and injunctive relief. On appeal, this court affirmed the finding of liability but reversed the awards of back pay and front pay to the class and remanded for the district court to fashion new class remedies in light of our opinion. See Pitre v. Western Elec. Co., 843 F.2d 1262 (10th Cir. 1988) ( Pitre I). The district court reformulated the amount of back pay and front pay by modifying its earlier approach in response to the errors we set out in Pitre I. See Estate of Pitre v. Western Elec. Co., 719 F. Supp. 966 (D.Kan. 1989) ( Pitre II). Both parties have again appealed. We affirm in part, reverse in part, and remand for further proceedings.

I.

The relevant facts and the prior course of this litigation have been exhaustively detailed in the opinions cited above. We therefore repeat only the background necessary to a consideration of the issues raised in this appeal.

In its first calculation of damages, the district court determined the number of women in each salary level that would have been promoted, downgraded, or laid off absent discrimination by using the percentage of women in each promotion or downgrade pool at the beginning of the back pay period. The court compared that figure with the number of women who were actually promoted, downgraded, or laid off. This difference was then translated to a back pay award by using the difference between the average earnings of men in the higher level and the average earnings of women in the lower level. In so doing, the court assumed that promotions were made only from the next lower level rather than from all lower levels. The district court recognized that using the actual work force in place at the beginning of the back pay period produced a lower back pay award than would have resulted by using a work force from which the effects of discrimination prior to this period had been factored out. However, the court stated its belief that this discrepancy could be remedied by awarding front pay. The court accordingly awarded front pay to continue until women comprised fifty percent of each salary level.

In the first appeal, we concluded that the district court had not adequately accounted for the lingering effects of discrimination in determining the amount of back pay. Pitre I, 843 F.2d at 1278. We rejected the court's attempt to remedy inadequate back pay with front pay, pointing out that front pay is a supplement to back pay, not a substitute for it. Id. at 1279. In remanding, we stated that the lower court was "free to consider any method of determining the appropriate amount of back and front pay to which the class is entitled." Id. However, we pointed out that

[b]y not using the women's current position in the company, the effects of past discrimination may be more fully incorporated into the formula. In principle, the district court's method of calculating the promotions that should have gone to women with those that actually did go to women could again be used. The court must, however, either attempt to account for the effect of past discrimination on the position of women at the beginning of the relevant period or explain why such consideration is unnecessary.

Id.

On remand, the district court again calculated the amount of back and front pay by comparing the promotions and downgrades that actually went to women with those that should have gone to women. In order to address its earlier failure to adequately allow for the cumulative effects of defendant's past discrimination, however, the court developed a "hypothetical workforce which would have been in place at the end of 1974 if the defendant had not discriminated against women in promotions and downgrades between 1965 and 1974." Pitre II, 719 F. Supp. at 971. In making comparisons, the court used this hypothetical 1974 work force, which attempted to eliminate the past discrimination, rather than the actual 1974 work force that the court had used previously, which embodied the effects of this discrimination. The court also awarded front pay to continue until women made up fifty percent of each salary level.

Both parties have again appealed. Plaintiff takes issue with the district court's method of calculating back and front pay, arguing that the court did not provide the most complete relief possible and did not adequately address the cumulative effects of defendant's past discrimination. In plaintiff's view, a proper back pay award should equal the difference between the total salary actually paid to women in salaried positions, and the percentage of the total salary paid to all salaried workers that women were proportionally entitled to receive. Thus, if women made up fifty percent of all salaried workers, they should receive fifty percent of the total salary less what they were actually paid. Plaintiff contends alternatively that, in constructing its hypothetical work force, the court erred in assuming that the proper promotion pool consisted of only the next lower level rather than all lower levels. Plaintiff argues that this alleged error resulted in an under-representation of women in the higher levels and a corresponding reduction in the number of promotions for which women received back pay. Plaintiff also contends that the lower court erred by awarding back pay only for the 180-day period prior to date on which plaintiff Pitre filed her charge, rather than using the two-year period set out in 42 U.S.C. § 2000e-5(g). Finally, plaintiff asserts that these alleged errors also infected the court's front pay award. In plaintiff's view, front pay should continue until women have received half of all promotions since 1965.

Defendant contends that the district court erred in failing to use a promotional pool that included hourly employees and other ungraded salaried employees who were not members of the plaintiff class. Defendant also takes issue with the court's decision to award front pay, and to continue that award until women make up half of each salary level.

II.

We begin our consideration of these arguments by noting, as we did in Pitre I, that considerable discretion is vested in the district court when devising remedies for Title VII violations. See generally Albemarle Paper Co. v. Moody, 422 U.S. 405, 416-422, 95 S.Ct. 2362, 2370-74, 45 L.Ed.2d 280 (1975). We also observe as we did earlier, however, that the district court's exercise of discretion in awarding back pay must be "measured against the purposes which inform Title VII." Id. at 417, 95 S.Ct. at 2371. Those purposes require a remedy that both provides an incentive to employers to avoid discriminatory practices, id. at 417-18, 95 S.Ct. at 2371-72, and makes "persons whole for injuries suffered on account of unlawful employment discrimination," id. at 418, 95 S.Ct. at 2372. Upon reviewing the district court's exercise of discretion on remand, all but one of the arguments raised in this appeal are easily resolved.

We find no abuse of discretion in the district court's selection on remand of the method by which it calculated back and front pay. We stated in Pitre I that the court could again compare promotions that should have gone to women with those that women actually received so long as the lingering effects of past discrimination were taken into account. See Pitre I, 843 F.2d at 1279. In choosing to use this comparison method, as modified, the district court rejected plaintiff's argument that women should instead receive their proportional share of the total amount of salaries, pointing out that

[a]t issue in this action are a finite number of identifiable decisions by the defendant regarding promotions and downgrades. We should focus these specific decisions and award the plaintiff damages when there is discrimination, rather than simply determining whether women received a pro rata portion of all salaries paid.

Pitre II, 719 F. Supp. at 970. We view this as an acceptable approach to the court's duty to provide compensation equal to the injury. See Albemarle, 422 U.S. at 418-19, 95 S.Ct. at 2372 (quoting Wicker v. Hoppock, 73 U.S. (6 Wall.) 94, 99, 18 L.Ed. 752 (1867)).

We likewise find no merit in both parties' objections to the district court's use of only the next grade as the promotion or downgrade pool in making comparisons. We held in Pitre I that the court's decision to calculate the amount of back pay on a step-by-step basis was not clearly erroneous, stating that although the district court was free on remand to reconsider its decision to assume that promotions would proceed one grade at a time, the court was not required to do so. See 843 F.2d at 1279 n. 11. Nothing presented in this appeal convinces us to disturb our prior ruling.

Equally unpersuasive are defendant's arguments with respect to front pay. We stated in Pitre I that the district court's decision to grant front pay was not an abuse of discretion. Id. at 1276. On remand, the court again concluded that front pay was appropriate and ordered it to continue until women comprised fifty percent of each salary level. The court was unpersuaded by defendant's argument that because promotion opportunities were virtually nonexistent, defendant was in effect precluded from ending its front pay liability. The court pointed out that "the lingering effects of past discrimination will continue to be felt until women constitute half of the work force for [a given] level." Pitre II, 719 F. Supp. at 974. The court preferred to place "the hardship of the present impossibility of correcting past discrimination on the defendant, the party found to have discriminated, rather than on the plaintiff, the victim of the discrimination." Id. The court's reasoning clearly implements both the deterrent and the "make whole" purposes of Title VII and accordingly is a proper exercise of discretion. See Albemarle, 422 U.S. at 419, 95 S.Ct. at 2372.

Finally, we address plaintiff's argument with respect to the appropriate period for purposes of computing back pay. Plaintiff contends that the district court should have calculated the amount of back pay on the basis of the two-year period provided by 42 U.S.C. § 2000e-5(g), rather than the 180-day period set out in 42 U.S.C. § 2000e-5(e). Although both of these periods are measured by the date a discrimination charge is filed with the EEOC, the periods serve different functions in the Title VII process. Section 2000e-5(e) establishes the limitation period for filing a discrimination charge with the EEOC, and requires that this charge must be filed "within one hundred and eighty days after the alleged unlawful employment practice occurred." Id. Claims based on events occurring prior to this 180-day period are ordinarily considered time-barred. Section 2000e-5(g), on the other hand, sets out the relief a district court may order upon a finding of discrimination, and provides inter alia, that "[b]ack pay liability shall not accrue from a date more than two years prior to the filing of a charge with the Commission." Id.

To establish substantive liability, a plaintiff must prove that at least one discriminatory act occurred within the 180-day period for filing a charge with the EEOC. See Furr v. AT T Technologies, Inc., 824 F.2d 1537, 1544 (10th Cir. 1987). That showing has clearly been made in this case. Once liability has been established, section 2000e-5(g) authorizes a district court to award back pay for the two-year period prior to the date the EEOC charge was filed. The court thus may award back pay measured by the two-year period of section 2000e-5(g) to remedy discriminatory acts that occur within the 180-day period of section 2000e-5(e).

In addition, this court has recognized the continuing violation theory, under which a district court may, in the requisite circumstances, provide a remedy for discriminatory acts occurring prior to the 180-day period of section 2000e-5(e). If the plaintiff establishes a pattern of continuing discrimination beginning before the 180-day period and extending into that period, the plaintiff may recover for those earlier acts.

Plaintiffs may bring suit for one or more discriminatory acts occurring before the limitations period, and may recover damages based on those injuries " if the plaintiff can demonstrate that the practice has actually continued into the `present' — that is, into the time period relevant to the date the charge of discrimination was filed. At least one discriminatory act must have occurred within the charge-filing period."

Furr, 824 F.2d at 1544 ( quoting Stewart v. CPC Int'l, Inc., 679 F.2d 117, 121 (7th Cir. 1982); see also Allen v. Denver Pub. Sch. Bd., 928 F.2d 978, 984 (10th Cir. 1991).

Plaintiff argued in the first appeal to this court that the district court erred by awarding damages measured only by the 180-day period of section 2000e-5(e). Although plaintiff argued to the district court on remand that damages should be calculated on the basis of the two-year period, the court without explanation failed to do so. Defendant contends that the district court's actions were not an abuse of discretion, asserting that this court in Pitre I implicitly approved the district court's use of the shorter period. We disagree. We simply did not address the issue in view of our general remand to allow the district court to reformulate its award under "any method" that accounted for the lingering effects of past discrimination. Pitre, 843 F.2d at 1279.

While recognizing that a plaintiff who establishes a continuing violation may recover for events occurring during the two-year period, Brief of Defendant-Appellee at 31, defendant makes an unfocused argument that to permit this recovery here would be inequitable. In support of its equity argument, defendant asserts that until plaintiff filed an amended complaint adding the class action, defendant had no notice that these acts would be the subject of a claim for relief because the original EEOC investigation focused only on the claim of the individual plaintiff. We do not find this argument persuasive, especially when defendant did not raise it at the appropriate time. We find no indication in the record on appeal that defendant opposed adding the class claims because they were so unrelated to the individual claim that a new EEOC charge was required. By failing to argue then that the class claims were different enough to require exhaustion, defendant has waived the argument now that the claims cannot therefore be fully remedied, particularly given the "`generally accepted principle that the scope of a Title VII lawsuit may extend to "any kind of discrimination like or related to allegations contained in the charge."'" Nealon v. Stone, 958 F.2d 584, 590 (4th Cir. 1992) (quoting Hill v. Western Elec. Co., 672 F.2d 381, 390 n. 6 (4th Cir.), cert. denied, 459 U.S. 981, 103 S.Ct. 318, 74 L.Ed.2d 294 (1982)); see also Brown v. Hartshorne Pub. Sch. Dist. No. 1, 864 F.2d 680, 682 (10th Cir. 1988).

Accordingly, defendant has not demonstrated in this appeal inequity that would preclude the district court from awarding damages under a continuing violation theory. This court, the district court, and the parties have all proceeded, until this late date, on the understanding that plaintiff's claims rest on a continuing violation theory. See Furr, 824 F.2d at 1544 (rejecting similar argument for same reasons). Indeed, the district court's creation of a hypothetical work force in its method of calculating damages is necessary precisely because of defendant's continuing practice of discrimination, which the court found to have existed in 1965 and to have continued into the 180-day filing period.

In addition, we observe that a plaintiff need not establish a continuing violation in order to receive damages for the two-year period. Section 2000e-5(g) authorizes the district court in its discretion to make such an award to any Title VII plaintiff. The discretion granted to district courts in awarding remedies for Title VII violations was intended by Congress "to make possible the `fashion[ing] [of] the most complete relief possible.'" Albemarle, 422 U.S. at 421, 95 S.Ct. at 2373. "[B]ackpay should be denied only for reasons which, if applied generally, would not frustrate the central statutory purposes of eradicating discrimination throughout the economy and making persons whole for injuries suffered through past discrimination." Id. Here, the district court did not award damages for the entire period authorized by Title VII and did not provide reasons for its failure to do so. If a district court declines to award back pay, "it [must] carefully articulate its reasons," id. at 421 n. 14, 95 S.Ct. at 2373 n. 14, so as to enable the court of appeals to test them against the purposes of Title VII, see id. at 421-22, 95 S.Ct. at 2373-74.

Accordingly, we must remand for the limited purpose of allowing the district court to address its failure to award back pay for the entire two-year period prior to the date the EEOC charge was filed. The court should either adjust its award or articulate its reasons for declining to do so. In ordering this limited remand, we emphasize that the only issue to be considered is the appropriate back pay period. We otherwise find no error or abuse of discretion in the remedies so carefully devised by the district court.

AFFIRMED in part, REVERSED in part, and REMANDED for further proceedings in light of this opinion.