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CALABRESI, Circuit Judge: Table of Contents Introduction.....................................................................70 Factual and Procedural Background................................................72 I. The Parties...........................................................72 II. General Factual Background............................................73 A. Custodians and Custodian Engineers ................................73 B. The Importance of Seniority........................................73 1. Transfers.....................................................74 2. Temporary Care Assignments...................................75 3. Layoffs.......................................................76 C. The Hiring Process................................................76 D. Provisional Employees.............................................77 III. The Government’s Investigation and Lawsuit..............................77 IV. The Settlement........................................................78 A. Settlement Terms.................................................78 B. Court Approval...................................................79 V. The Settlement Is Implemented................. 80 VI. The Second Circuit Vacates and Remands................................80 VII. Proceedings on Remand................................................81 A. The Brennan Plaintiffs Intervene and File a Related Complaint.........81 B. The Government Changes Its Position; Offeree Interventions Result.........................................................82 VIII. The District Court’s Opinions...........................................83 A. The September 11, 2006 Opinion ....................................83 B. The April 20, 2007 Opinion .........................................86 C. The May 28, 2008 Opinion..........................................87 IX. The Miranda Lawsuit..................................................89 X. The Stay Applications..................................................89 Discussion.......................................................................89 I. Title VII Background..................................................89 II. Procedural Posture and Standard of Review..............................91 III. Prima Facie Case and Defenses.........................................92 IV. Affirmative Action.....................................................96 A. Legal Background.................................................96 B. Application of Johnson and Weber to the Settlement Agreement......97 1.Ricci.........................................................97 ' 2. Is the Implementation of the Settlement Agreement an Affirmative Action Plan?......................................99 a. What Is an Affirmative Action Plan?..........................99 b. The Employer Action in This Case..........................104 V. Strong Basis in Evidence..............................................109 A. What Is a Strong Basis in Evidence?................................110 1. Strong Basis in Evidence of Liability............................110 2. Strong Basis in Evidence of Necessity...........................113 B. The Government’s “Actual Violation” Standard.......................114 1. Ricci Does Not Require a Showing of Actual Liability or Actual Victims....................................................115 2. The Consent-Decree, Settlement-Approval, and § 706(g) Cases Do Not Apply in the § 703(a) Context...................116 3. The Brennan Plaintiffs Have Another Remedy for Any Breach of Contract by the City Defendants...........................120 VI. Application of the Strong-Basis-in-Evidenee Standard....................124 A. Prima Facie Case................................................125 1. Testing Discrimination........................................125 2. Recruiting Discrimination......................................125 B. Job-Related and Less Discriminatory Alternative....................127 C. Necessity and Make-Whole Relief..................................128 VII. Equal Protection.....................................................134 VIII. Class Certification....................................................136 IX. Remedies ...........................................................137 X. Conclusion...........................................................140 Introduction In 1996, the United States (the “Government”) sued the New York City Board of Education and related parties (the “City Defendants”) claiming a violation of Title VII’s prohibition of disparate impact selection measures. The suit alleged that the City had, in hiring Custodians and Custodian Engineers (“CEs”) for its schools, (1) used, on three separate occasions, civil service examinations which discriminated against blacks and Hispanics, and (2) used recruiting practices which discriminated against blacks, Hispanics, Asians, and women. The parties entered into a settlement agreement in 1999 and asked the district court to enter it as a consent decree. The magistrate judge (Levy, M.J.) — who had jurisdiction by consent— approved the entire agreement, despite objections that primarily came from incumbent employees who were denied leave to intervene in the suit. The incumbent employees were unaffected by many of the agreement’s provisions, but they objected to four paragraphs that provided permanent appointments and retroactive competitive seniority to 63 black, Hispanic, Asian, or female individuals, the “Offerees.” The City Defendants implemented the disputed parts of the settlement while the incumbent employees’ appeal from their exclusion was pending. In 2001, this Court vacated and remanded, holding that the district court should have permitted the incumbent employees to intervene. After the remand, the incumbent employees asked the district court to have the case sent to a district judge rather than the magistrate judge; this request was granted. They then brought two reverse-discrimination lawsuits against the City under § 703(a) of Title VII and the Equal Protection Clause (via 42 U.S.C. § 1983); these cases were consolidated with the original 1996 Government lawsuit. The new lawsuits sought equitable relief and damages. The incumbent employees also requested class certification. Meanwhile, the Government decided that it would defend the settlement agreement only in part. This prompted two groups of beneficiaries of the settlement to intervene to defend the retroactive seniority that the settlement had granted them. One group, the Arroyo Intervenors, consisted of ten Offerees who had taken and failed a challenged exam; the other group, the Caldero Intervenors, consisted of twenty-two Offerees who had not taken any challenged exam. After years of contentious litigation, extensive discovery, and a set of three opinions spanning a total of approximately 150 pages, the district court (Block, J.) entered a final judgment. It held that some of the retroactive seniority provided by the settlement agreement violated Title VII, and that some of the retroactive seniority that did not violate Title VII violated the Equal Protection Clause. But, the court concluded that a significant remainder of the retroactive seniority was lawful. In particular, the court held (1) that the retroactive seniority of the test-failer Offerees did not violate Title VII or the Equal Protection Clause, except insofar as layoff seniority was granted to individuals who were not actual victims of discrimination; (2) that some of the test-failers were actual victims and others were not; (3) that the female non-test-failer Offerees’ retroactive seniority did not violate Title VII or the Equal Protection Clause, except that their layoff seniority violated both Title VII and the Equal Protection Clause since — because there was no prima facie case of recruiting discrimination with respect to them — none of them were actual victims of such discrimination; and (4) that the minority male non-test-failers’ retroactive seniority did not violate Title VII, but did violate the Equal Protection Clause. As a remedy the court entered a declaratory judgment, accompanied by schedules specifying the extent to which each individual’s retroactive seniority was lawful. The class of incumbent employees was also certified, but their damage claims were rejected. Finally, the district court declined to enter any part of the disputed paragraphs of the settlement agreement into a consent decree. On appeal, the district court’s refusal to enter a consent decree is not challenged. The only disputes before us are the incumbent employees’ lawsuits, which claim that the City Defendants’ (voluntary) implementation of the settlement agreement violated § 703(a) of Title VII and 42 U.S.C. § 1983. The Title VII claim requires us to decide the applicability of Ricci v. DeStefano, — U.S. -, 129 S.Ct. 2658, 174 L.Ed.2d 490 (2009), which was decided after the district court issued its decision in this case. The district court’s Title VII analysis was based on the “affirmative action” framework of Johnson v. Transp. Agency, Santa Clara County, 480 U.S. 616, 107 S.Ct. 1442, 94 L.Ed.2d 615 (1987), and United Steelworkers of Am. v. Weber, 443 U.S. 193, 99 S.Ct. 2721, 61 L.Ed.2d 480 (1979). We hold that, contrary to the preRicci law in this Circuit, Johnson and Weber do not apply to all race- or gender-conscious employer actions. In light of Ricci, the “manifest imbalance” and “no unnecessary trammeling” analysis of those cases extends, at most, to circumstances in which an employer has undertaken a race- or gender-conscious affirmative action plan designed to benefit all members of a racial or gender class in a forward-looking manner only. Where, as here, the employer instead provides individualized race- or gender-conscious benefits as a remedy for previous disparate impact, the employer must satisfy the requirements of Ricci, not Johnson and Weber, in order to avoid disparate-treatment liability. Under Ricci, the employer must show a strong basis in evidence that, at the time the race- or gender-conscious action was taken, the employer was faced with disparate-impact liability and that the race- or gender-conscious action was necessary to avoid or remedy that liability. In addition to our central holding, we address several other issues. We discuss a few matters related to the identification of those individuals who, the City Defendants had a strong basis in evidence to believe, were victims of disparate impact and, therefore, as to whom the retroactive-seniority provided in the settlement agreement was a proper remedy. We also discuss what remedies the district court might properly consider, and we advise the district court that while it may be appropriate to strip certain settlement beneficiaries of the retroactive seniority they received from the settlement agreement, it is not correct to strip them of seniority stemming from their permanent appointments. Because it is possible that the case can be resolved on Title VII grounds, we decline at this time to address the important and difficult Equal Protection Clause questions that attach to the case. Finally, we affirm the district court’s grant of class certification because, in so certifying, the district court did not abuse its discretion. Accordingly, we AFFIRM the district court’s judgment in part, VACATE it in part, and REMAND the case for further proceedings consistent with this opinion. Factual and Procedural Background I. The Parties This appeal stems from three lawsuits involving five parties or groups of parties, who, from different directions, attack just about every aspect of the district court’s judgment. The incumbent employees (the “Brennan Plaintiffs”) have appealed, and the Caldero Intervenors and the Government have cross-appealed. Since the City Defendants have withdrawn their cross-appeal and have not submitted briefs, the four parties before us are: • The Brennan Plaintiffs, who seek to invalidate as much of the four challenged paragraphs of the settlement as possible. • The Arroyo Intervenors, who seek to defend the settlement for Offerees who failed a challenged exam. • The Caldero Intervenors, who seek to defend the settlement for Offerees who did not take any challenged exam. • The Government, which wishes to defend some portions of the settlement, but not others. II. General Factual Background The focus of the Government’s 1996 lawsuit was the allegedly discriminatory hiring of Custodians and Custodian Engineers by the City Defendants. A. Custodians and Custodian Engineers The Board of Education (the “Board”) employs Custodians and Custodian Engineers to take care of the approximately 1200 buildings in the City’s school system. Custodian and CE positions are desirable supervisory jobs with good pay and civil-service protections. Each Custodian or CE is assigned to a school, and he or she supervises all the handymen and cleaners at that school. The Custodian or CE also has the responsibility for the upkeep, cleanliness, and safety of the assigned school. The main difference between Custodians and CEs is that CEs have more experience and a difficult-to-obtain stationary engineer’s license. During the times at issue in this case, the Board employed over 900 Custodians and CEs. Custodians and CEs are paid through a century-old, arcane, and idiosyncratic system known as the “indirect system.” See generally Beck v. Bd. of Educ. of City of New York, 268 A.D. 644, 646-47, 52 N.Y.S.2d 712 (N.Y.A.D.2d Dep’t 1945). Under this system, the Custodian or CE is both a civil servant and an independent contractor. The Board allots each Custodian a lump sum of money based on the size and other characteristics of the assigned school. The Custodian uses some of this money to hire cleaners and helpers and to pay for supplies, and, up to a specified limit, he retains the rest for himself. The Board does not tell Custodians how to clean and maintain things or whom to hire; it only tells them whether the school is being cleaned and maintained satisfactorily. Custodians and CEs thus, purportedly, have an incentive to maintain their schools adequately but in a cost-effective manner. Id. B. The Importance of Seniority The seniority of a Custodian or CE is important in several ways, only three of which are relevant to the appeal before us: seniority improves a Custodian or CE’s ability (1) to get transfers to more desirable schools; (2) to get Temporary Care Assignments (“TCAs”); and (3) to avoid being laid off. At least for transfers and layoffs, the effect of seniority is specified in a collective bargaining agreement between the Board and the union representing Custodians and CEs, Local 891 of the International Union of Operating Engineers (“Local 891”). Before discussing those matters, it is worth noting one way in which seniority is not at issue in this appeal: some seniority (which is termed “non-competitive” seniority) concerns a Custodian or CE’s relationship with the Board in ways that do not affect the holder of that seniority’s relationship to other Custodians or CEs. For example, the seniority that affects the amount of pay a Custodian or CE receives is, in this sense, “non-competitive.” See supra note 8. 1. Transfers Because Custodians and CEs earn higher salaries when they work in larger schools, it is desirable, when the opportunity arises, for them to transfer to larger schools. When there is a vacancy at a school, seniority plays a crucial role in determining who gets the transfer. Pursuant to the “rating and transfer plan” in the collective bargaining agreement for Custodians and CEs, each school in the system is assigned to a particular “seniority bracket” based on its square footage. CE brackets are associated with larger schools than the brackets for Custodians who have the same level of experience. In addition, some schools are available only to CEs, while some other schools are available to Custodians only if the Custodians have a refrigeration license. Every few months or so, as needed, the Board issues a Vacancy List to Custodians and CEs. The Vacancy List sets out the schools with a Custodian or CE vacancy, and any Custodian or CE who is eligible to transfer may bid for open schools and specify his or her order of preference. Custodians and CEs may bid for a school above their seniority bracket, so long as the bidder is not a Custodian bidding for a CE-only school, or a Custodian without a refrigeration license bidding for a school that requires such a license. Then the Board looks at who has applied for each vacant school. If only one eligible person bids for a school, then that person gets the school. The vast majority of vacant schools do not result in competition; either nobody or only one person bids for them. The most desirable vacancies, however, receive multiple bids. In such cases, if at least one bidder is in or above the school’s seniority bracket, then any Custodian or CE who is below that seniority bracket will not get the school. In other words, a Custodian or CE can never get a school above his or her seniority bracket unless nobody in or above the required seniority bracket applies for the vacancy. If two or more candidates are in or above the required seniority bracket, then the transfer generally goes to the applicant with the highest performance rating from his or her current school’s principal. However, if any other candidate’s performance rating is within .25 points of the top candidate’s performance rating, then seniority is used as a tie-breaker between them. The vacant school’s principal can veto a Custodian or CE, but this does not appear to be a frequent occurrence. Indeed, nothing in the record indicates that it has ever happened. Once an applicant is determined by the Board to be the top applicant for a vacant school, the applicant cannot withdraw his or her bid; transfer to that school is mandatory. About 1% of the schools in the entire system get a new Custodian or CE each time the transfer process occurs. 2. Temporary Care Assignments Seniority also affects Temporary Care Assignments — though only slightly. When a temporary school vacancy results from illness, vacation, or leave, the Board fills the vacancy through the TCA process. Unlike the transfer process, the TCA process is not found in the collective bargaining agreement. The record conflicts as to whether the TCA process is governed by any contract negotiated with Local 891. A Custodian or CE who receives a TCA will, for the duration of the TCA — usually two months — look after the TCA school in addition to his or her regularly assigned school. During that time, the salary of the Custodian or CE will be increased by 75% — or 100% in the unlikely event that the TCA lasts more than six months — even though he or she is not required to put in any additional time on the job. A Custodian or CE can reasonably expect to get a TCA once every two years. The process for assigning TCAs is somewhat different from the transfer process, but seniority still plays a role. The record is, however, unclear as to how significant that role is. Once a Custodian or CE has at least one year of experience, he or she is added to the TCA waitlist for the district in which his or her regularly assigned school is located, or for adjacent districts. As TCAs arise, they are assigned to the Custodian or CE at the top of the list, so long as the TCA school does not require a license or special skill that the top person does not have. Upon finishing the TCA, the Custodian or CE is returned to the bottom of the list. Because of the rotation system, seniority seems to play only a relatively minor role in the awarding of TCAs. The district court does, however, suggest a way in which seniority might make a difference. According to that court, there are three separate TCA lists in each district: one for CEs, one for Custodians with at least 15 years’ seniority, and one for other Custodians. United States v. N.Y. City Bd. of Educ., 448 F.Supp.2d 397, 411-12 (E.D.N.Y.2006) [hereinafter NYC Board III]. None of the parties’ briefs mentions three lists, nor do these briefs cite any part of the record supporting this proposition. But, if the district court’s statement is correct, then increasing a Custodian’s seniority might increase the size of the 15-year TCA list and thereby work to the detriment of other Custodians on that list. This would correspondingly benefit other Custodians who are on the fewer-than-15years TCA list by decreasing that list’s length. Similarly, it is to the advantage of any particular Custodian or CE for there to be as few as possible other Custodians or CEs with at least one year of seniority in the same or adjacent districts. For then it would not take as long to get back to the top of the list after a TCA assignment. 3. Layoffs Seniority directly determines the order in which Custodians or CEs will be laid off under N.Y. Civ. Serv. Law § 80(1). The statute and the CBA provide for a typical “last hired, first fired” system. C. The Hiring Process During the disputed period, the hiring process included four steps for Custodians and three steps for CEs. First, because a Custodian or CE is a civil servant within the “competitive class” as defined under New York law, an applicant wishing to become a Custodian or CE had to pass a civil service examination. The City Defendants administered three disputed exams: (1) Exam 5040, which was given in 1985 for the Custodian position; (2) Exam 8206, which was given in 1989 for the CE position; and (3) Exam 1074, which was given in 1993 for the Custodian position. Second, an applicant had to submit “experience papers” explaining how the applicant satisfied the minimum qualifications for the position. The minimum qualifications — a few years of relevant experience for a Custodian, and a few more years plus the coveted high-pressure boiler license (also known as a “stationary engineer license”) for a CE — were stated in the notice for each of the aforementioned, disputed, exams. Once the exam was administered, the City Defendants reviewed the experience papers for passing applicants. A finding of insufficient experience could be administratively appealed. The exact proportion of appeals that overturned the City Defendants’ original findings is unclear and disputed, but the proportion of successful appeals clearly was not insignificant. Third, for Exams 5040 and 1074 (the Custodian exams), but not for Exam 8206 (the CE exam), a practical test was required. The Exam 5040 practical was oral and it was given only to those applicants who had both passed the civil service exam and had had their experience papers accepted. Applicants were taken to the boiler room in a school in Brooklyn and asked questions about what they would do under various circumstances. For Exam 1074, this practical test was changed to a written format, so that the City Defendants could make sure that each applicant was asked the same questions. Also, unlike the Exam 5040 practical, the practical for Exam 1074 was administered — and individuals who failed it were eliminated — before the experience papers were reviewed. A small but non-trivial percentage of applicants failed the practical test. After these steps were completed, applicants who had passed the written exam, the “experience papers” stage, and the practical exam (if applicable), were placed on an “eligible list,” starting with the highest scorers on the written exam and ending with the lowest passing scorers. When the Board needed a Custodian or CE, it would follow the “Rule of Three.” Under this rule, it would call the top few people (usually three, but sometimes more if there were more than one vacancy) on the eligibility list for interviews. See N.Y. Civ. Serv. Law § 61(1). The vacancy or vacancies would then be filled by whichever ones of the interviewees were selected by the interviewers. Applicants who were interviewed three times without being hired would be removed from the eligibility list. The Board hired Custodians from the Exam 5040 eligibility list from Spring 1987 through Fall 1990. The Exam 8206 eligibility list was used to hire CEs from Spring 1991 through early 1994, and the Exam 1074 eligibility list was used for Custodians from early 1997 through early 2000. D. Provisional Employees In addition to the permanent Custodians and CEs, who had to go through the above described process and who had competitive seniority and civil-service protections, the City Defendants hired “provisional” Custodians and CEs. Provisional Custodians and CEs can be fired at any time, do not accrue competitive or non-competitive seniority, cannot bid for transfers to other schools, cannot obtain TCAs, and have to work wherever the Board puts them. It is therefore much better to be a permanent Custodian or CE than to be a provisional one. But provisional Custodians and CEs have the same responsibilities at the schools to which they are assigned as then-permanent counterparts. And they are supposed to have the same experience and, in the case of provisional CEs, the boiler license as well. Provisional Custodians and CEs are hired when the Board needs Custodians and CEs but there is no appropriate eligibility list from which to hire permanent employees. See N.Y. Civ. Serv. Law § 65. III. The Government’s Investigation and Lawsuit The U.S. Department of Justice began to investigate possible discrimination in the hiring of permanent Custodians and CEs in the early 1990s. A 1993 demographic survey revealed that more than 99% of the permanent Custodian and CE workforce was male, and 92% was white. In contrast, blacks constituted about 20% of the qualified labor pool for these positions, Hispanics made up about 19% and women about 8% of the pool. A 1996 demographic survey showed similar results. It also appeared (as was later confirmed by the investigation) that racial minorities and women were much more likely to be hired as provisional Custodians or CEs than as permanent Custodians or CEs, even though the qualifications for both were the same. These data aroused the Government’s suspicion that something in the permanent hiring process was discriminatory. Based on a statistical analysis of the results of the investigation, the Government sued the City Defendants on January 30, 1996. The Government originally made both pattern-and-practice claims (which require proof of intentional discrimination) and disparate-impact claims. But it ultimately pursued only the disparate-impact claims. Two sets of these were asserted. In the first, the Government alleged that some of the tests employed brought about discriminatory results. Specifically, the claim was that Exams 5040, 8206 and 1074 had a disparate impact on blacks and Hispanics. This allegation was based on a report from two statisticians, who concluded that the statistical significance of the disparities in passage rates between white, black, and Hispanic takers of those three exams was overwhelming — it ranged from 2 to nearly 14 standard deviations. See NYC Board III, 448 F.Supp.2d at 407. The second set of claims, the recruiting claims, alleged that the City Defendants’ recruiting practices had a disparate impact on blacks, Hispanics, Asians, and women. In support of these claims, the Government produced a report by Dr. Orley Ashenfelter, a labor economist. The report said that the number of blacks, Hispanics, Asians, and women who took each of the three disputed exams was lower than the number that would be expected based on the representation of qualified individuals in the overall labor pool. Dr. Ashenfelter found that the differences were statistically significant at the 5% level, and for some groups the probability that the differences were the result of chance was much lower. Although Dr. Ashenfelter did not offer any opinion as to the cause for these disparities, the Government asserted that they resulted from limited advertising and word-of-mouth referrals that had a disparate impact on women and minorities. IV. The Settlement By 1999, extensive discovery had been conducted, but the Government had not moved for summary judgment and the case had not gone to trial. Before the Government had attempted to prove its case in court, the Government and the City Defendants entered into settlement negotiations, which concluded with the signing of a settlement agreement. Although much of the agreement did not give rise to any objections from third parties, four paragraphs, numbered 13-16, came under attack. Only those four paragraphs, and the consequences of their implementation, are at issue on this appeal. A. Settlement Terms Paragraph 13 provided that all “Offerees” who were serving as provisional Custodians or CEs as of the date the court approved the settlement agreement would be granted equivalent permanent positions. “Offeree” was defined earlier in the agreement to include two groups: (a) all black, Hispanic, Asian, or female individuals who were employed as permanent or provisional Custodians or CEs as of the date of approval of the agreement; and (b) all black, Hispanic, Asian, or female individuals who had taken one of the challenged exams and had been hired as provisional Custodians or CEs after the date of the agreement but before court approval of the agreement. The list of the 54 people falling into group (a) was attached as Appendix A to the agreement. Paragraphs 14-16 gave the Offerees retroactive seniority in accordance with the following terms: • For any Offeree listed in Appendix A of the agreement who had not taken a challenged exam, the retroactive seniority date was the date of his or her provisional hiring. • For any Offeree listed in Appendix A of the agreement who had taken a challenged Custodian exam, the retroactive seniority date was the earlier of (i) his or her provisional hiring date, or (ii) the “Median Date” for the challenged exam that he or she took, provided that if he or she had taken more than one exam then the earlier median date applied. • For Offerees not listed in Appendix A of the agreement — those Custodian Offerees in group (b), ie., those hired as provisionals after the agreement but before court approval of it — the retroactive seniority date was the earliest provisional hire date for that Offeree’s job title, as listed in an earlier stipulation regarding provisional hires. Thus, if the Offeree was a provisional Custodian, he or she would get the earliest provisional hire date for Custodians, which was February 28, 1992. If the Offeree was a provisional CE, he or she would get the earliest provisional hire date for CEs, which was April 13,1990. The agreement provided that the retroactive seniority dates would “apply for all purposes for which seniority is applied except any applicable probation requirement.” Accordingly, in addition to the TCA, transfer, and layoff benefits that are in dispute, the seniority dates provided various non-competitive benefits, which are not at issue here. B. Court Approval After the Government and the City Defendants agreed to the settlement, it went to Magistrate Judge Levy — to whose jurisdiction, as mentioned earlier, the parties had consented pursuant to 28 U.S.C. § 636(c) — for a fairness hearing, because the parties sought to have the agreement entered as a consent decree. See United States v. N.Y. City Bd. of Educ., 85 F.Supp.2d 130, 135 (E.D.N.Y.2000) [hereinafter NYC Board I ], vacated and remanded, Brennan v. N.Y.C. Bd. of Educ., 260 F.3d 123 (2d Cir.2001) [hereinafter NYC Board II]. The district court gave notice and opportunity to object. Cf. 42 U.S.C. § 2000e-2(n) (preventing subsequent challenges to employment practices implementing a consent judgment if notice and opportunity to object have been given). There were over 300 objections, about half of which were form letters. NYC Board I, 85 F.Supp.2d at 134 & n. 3. Three objectors, who were white male incumbent permanent Custodians or CEs, moved to intervene: John Brennan, James G. Ahearn, and Kurt Brunkhorst. Id. at 134-35. The Magistrate Judge determined that the Government had made out a prima facie case of disparate impact for both the testing and recruiting claims. Id. at 141-45. Next, he determined that the settlement was fair and reasonable. He rejected the objections of Brennan et al., along with other objections not relevant here. In particular, he noted that the settlement “avoided the need for a complex, expensive, and lengthy trial,” and that extensive discovery had already taken place. Id. at 146. He also said that the settlement was consistent with the objectives of Title VII; and that, although it was the Board and not Brennan, Ahearn, and Brunkhorst who bore the responsibility for the past discrimination the suit and agreement sought to correct, the effect of the Offerees’ retroactive seniority on existing permanent Custodians and CEs was minimal. Id. at 146-51. Finally, the Magistrate Judge rejected the argument of Brennan et al. that they were entitled to intervene as of right pursuant to Federal Rule of Civil Procedure 24(a)(2). The court concluded that they did not have a protected interest in their seniority because (1) the remedies afforded the Offerees were “designed only to return employees to the positions they would have been in but for the alleged discrimination,” NYC Board I, 85 F.Supp.2d at 155, and (2) the possibility that the Offerees’ retroactive seniority would affect the would-be intervenors was too “remote and speculative” to constitute a cognizable interest, id. at 156. Accordingly, the Magistrate Judge approved the settlement and denied the motion to intervene. Id. at 157. V. The Settlement Is Implemented Shortly after the Magistrate Judge’s approval of the settlement, the City Defendants began implementing the agreement. They notified 63 Offerees — the 54 individuals listed in Appendix A to the agreement, plus nine other individuals — that they were entitled to relief under the agreement, if they agreed to release all discrimination claims against the City Defendants. 59 Offerees took the settlement, three resigned, and one declined the settlement. These 59 Offerees received permanent status, retroactive seniority, or both. For transfer and layoff purposes, the retroactive seniority operated as one would expect. The Offerees’ retroactive seniority was effective for both the seniority-bracket stage and the tie-breaker stage of the transfer process. And if layoffs were ever to occur, Offerees would be treated for purposes of the last-hired, first-fired rule as having been hired on their retroactive seniority dates. For TCA purposes, however, it is unclear what happened to Offerees who got retroactive seniority. As the district court pointed out, the record is contradictory as to (1) whether Offerees who were already permanent employees immediately went to the top of the list or stayed where they were, and (2) whether Offerees who were not permanent employees, or who had been permanent employees for less than one year at the time they accepted the settlement, were put at the top or the bottom of the list upon completing their probationary periods. See NYC Board III, 448 F.Supp.2d at 412 & n. 22. It is, however, clear that, as provided in the settlement agreement, the Offerees had to wait out a one-year probationary period before they were added to the TCA lists. VI. The Second Circuit Vacates and Remands Brennan, Ahearn and Brunkhorst appealed the Magistrate Judge’s decision to this Court. In August 2001, we vacated and remanded with instructions for the district court to permit the Brennan Plaintiffs to intervene. NYC Board 11, 260 F.3d at 133. We held that the Magistrate Judge had misapplied Federal Rule of Civil Procedure 24(a)(2). First, we rejected the Magistrate Judge’s argument that the Brennan Plaintiffs’ seniority rights were presumptively the result of illegal discrimination, because it “put the cart before the horse.” Id. at 129. Second, we held that an employment civil rights plaintiff or intervenor does not have to show a property interest in his job or its attributes in order to intervene; rather, “where a proposed intervenor’s interests are otherwise unrepresented in an action, the standard for intervention is no more burdensome than the standing requirement.” Id. at 131. Third, we held that “because the exercise of seniority rights has a domino effect,” a Brennan Intervenor’s “loss of a desirable transfer need not be directly to an Offeree ... for the loss to be the result of the [settlement] Agreement.” Id. at 132. Therefore, since the Board did not adequately represent the Brennan Plaintiffs’ interests, the district court should have allowed them to intervene. Id. at 132-33. We declined, however, to address the merits of the case: Appellants also ask us to exercise discretionary jurisdiction and rule on the merits of the Agreement, rather than remand the case to the district court____ We think such a course would be ill-advised. Appellants have argued convincingly that they were denied the opportunity to develop a record that would have permitted a full and appropriate ruling on the fairness and constitutionality of the Agreement. Given the heavily factual nature of these issues, we believe that the best course is to remand the case to allow for a full development of the record. Id. at 133 (citation omitted). VII. Proceedings on Remand After remand, this case lingered in the district court for about eight years, in the course of which several significant things happened: (1) the Brennan Plaintiffs filed two cases that were consolidated with the main case; (2) the Government began to attack parts of the settlement agreement; (3) the Caldero and Arroyo Intervenors entered the case in response to the Government’ change of position; (4) additional discovery and hearings took place; and (5) the district court issued a set of decisions upholding most, but not all, of the settlement against the reverse-discrimination attacks brought by the Brennan Plaintiffs, but declining to approve the settlement as a consent decree. A. The Brennan Plaintiffs Intervene and File a Related Complaint In October 2001, on remand, the Brennan Plaintiffs, having been permitted to intervene, filed a Complaint in Intervention alleging primarily that the retroactive grants of seniority in paragraphs 13-16 of the settlement agreement violated Title VII and the Equal Protection Clause. The Government moved to dismiss these claims in November 2001. On February 28, 2002, before that motion was fully briefed, Magistrate Judge Levy approved the undisputed portions of the settlement agreement, with consent of the parties. Because of certain arguments raised in the Government’s motion to dismiss, and because the Brennan Plaintiffs wanted to add two new individuals with damage claims (John Mitchell and Eric Schauer), the Brennan Plaintiffs, not satisfied simply to intervene, filed an action on January 11, 2002 (“Brennan”). In this suit, Mitchell and Schauer claimed that, in violation of Title VII and 42 U.S.C. § 1983, they had each lost a transfer to an Offeree because of the City Defendants’ implementation of the settlement agreement. In addition to the damage claims, all the Brennan Plaintiffs sought declaratory and injunctive relief against the City Defendants, DOJ, and the Attorney General. The Brennan case was eventually consolidated with the Government’s case in November 2003. B. The Government Changes Its Position; Offeree Interventions Result On April 8, 2002, the Government filed a memorandum in response to the Brennan Plaintiffs’ February 2002 motion for a preliminary injunction. In this memorandum, the Government only partially opposed the motion. The Government opposed a preliminary injunction against the settlement as to Offerees who had taken a challenged exam, but not as to Offerees who had not. Two days later, the Government withdrew its previous counsel and substituted new counsel. Next, the City Defendants moved for approval of the remaining paragraphs of the settlement agreement, and the Government opposed this motion as “premature.” In July 2002, a recruiting-claim beneficiary, Janet Caldero, learned that the Government was no longer defending the settlement as to Offerees such as she. She and others in her situation, having obtained counsel, moved to intervene in October 2002. The parties agreed to the 22 Caldero Intervenors’ intervention in February 2003. Around this time, the Brennan Plaintiffs also invoked their rights as parties to object to the magistrate judge’s 28 U.S.C. § 636(c) jurisdiction 2 to render a final decision, and, as a result, the case was returned to Judge Block. Then, in September 2003, the Government changed its position again, triggering yet another intervention. In response to some interrogatories during discovery, the Government provided a chart detailing its current thinking about which Offerees were entitled to retroactive competitive seniority. This chart indicated for the first time that, in addition to the 32 Offerees who had not taken an exam, as to most of whom the Government had already indicated that it would not be defending the settlement, the Government would now also not be defending the settlement as to some (but not all) Offerees who had taken a challenged exam. Although the Government did not say that this latter group of Offerees was not entitled to any retroactive seniority, it did say that, for competitive seniority purposes, these individuals were entitled only to retroactive seniority dates later — usually by about two years— than those provided for by the settlement agreement. The chart also denominated the Offerees who had not taken an exam as “recruiting claimants,” and the others as “testing claimants.” That is, the Government separated the Offerees into two groups, based on the stage of the hiring process at which they allegedly suffered discrimination. Having learned of this document, some of the affected Offerees (the Arroyo Intervenors) moved to intervene. Their motion was granted in July 2004. See NYC Board III, 448 F.Supp.2d at 417. VIII. The District Court’s Opinions After further discovery, the Brennan Plaintiffs and the Arroyo and Caldero Intervenors cross-moved for partial summary judgment. Additionally, the City Defendants moved to enter the settlement agreement as a consent decree, and the Brennan Plaintiffs moved for class certification. The district court issued its first of three opinions on September 11, 2006. See NYC Board III, 448 F.Supp.2d 397. Some issues of fact remained, however. After a hearing on those facts, the district court issued its second opinion on April 20, 2007. See United States v. N.Y. City Bd. of Educ., 487 F.Supp.2d 220 (E.D.N.Y.2007) [hereinafter NYC Board IV]. After another hearing dealing with still remaining fact questions, the district court issued its third opinion on May 28, 2008. See United States v. N.Y. City Bd. of Educ., 556 F.Supp.2d 202 (E.D.N.Y.2008) [hereinafter NYC Board V]. Final judgment was, at long last, entered on August 18, 2008. A. The September 11, 2006 Opinion In its 2006 opinion, the district court considered first whether the settlement awards violated Title VII, and then whether they violated the Equal Protection Clause. The court concluded: • As to the 28 black or Hispanic Offerees before the district court in 2006 who had taken and failed a challenged exam: • The lawfulness of one Offeree’s retroactive seniority could not be determined because there was a genuine issue of material fact as to whether Exam 8206 had a disparate impact on Hispanics; a hearing was required on that issue. • Seven Offerees were actual victims of discrimination and their entire retroactive seniority was lawful. • There were factual disputes as to whether the remaining twenty Offerees were actual victims of discrimination, but their retroactive seniority for TCAs and transfers was lawful regardless of whether they were actual victims. Their retroactive layoff seniority, however, was lawful only if they were actual victims. • As to the 31 black, Hispanic, Asian, or female Offerees before the district court in 2006 who had not taken a challenged exam and/or were not among the groups on which those exams allegedly had a disparate impact: • One Offeree was really a white male. His retroactive seniority was unlawful. • The retroactive seniority of the other 11 male non-test-taker Offerees was unlawful unless they could show that they were actual victims of discrimination. According to the district court, giving them relief without such a showing would violate the Equal Protection Clause. • The 19 female non-test-taker Offerees could lawfully receive full retroactive seniority for transfer and TCA purposes, but not for layoffs. NYC Board III, 448 F.Supp.2d at 446-47. The court’s reasoning was as follows. First, it addressed a preliminary issue: whether the Brennan Plaintiffs were correct in their assertion that five supposedly Hispanic Offerees were not entitled to any relief because they were not in fact Hispanic. Relying on the EEOC’s definition of “national-origin discrimination” in 29 C.F.R. § 1606.1, the district court held that “an ancestral place of origin is sufficient to establish membership in a protected class.” NYC Board III, 448 F.Supp.2d at 422. Applying that definition, the district court held that one recruiting claimant, Ciro Dellaporte, was not Hispanic. Id. The other four — Kevin LaFaye, Steven Lopez, and the brothers Nicholas Pantelides and Anthony Pantelides, were Hispanic “because LaFaye’s father and the Pantelides’ mother were born in Puerto Rico, and Lopez’s grandfather was born in Mexico.” Id. Next, the district court sought to determine whether the retroactive seniority awards violated the Brennan Plaintiffs’ rights under Title VII. The district court relied heavily on the “affirmative action” framework of Johnson, 480 U.S. 616, 107 S.Ct. 1442, and Weber, 443 U.S. 193, 99 S.Ct. 2721, consistent with which an employer defending an affirmative-action plan against a Title VII reverse-discrimination challenge needs to show only that (1) there is a “manifest imbalance” in a traditionally segregated job category and (2) the plan does not “unnecessarily trammel” the interests of adversely affected third parties. NYC Board III, 448 F.Supp.2d at 423-24. The district court rejected the Brennan Plaintiffs’ argument that the Weber/Johnson framework did not apply. Id. at 428-31. According to the district court, “there is nothing in Title VII that vitiates an affirmative-action plan granting preferential seniority to non-victims of discrimination.” Id. at 429. Applying the “affirmative action” framework, the district court found a manifest imbalance for both non-test-taker and testfailer Offerees. For the Offerees who had failed a test, the district court said that the Government had satisfied the “manifest imbalance” requirement by showing statistical evidence sufficient to make out a prima facie case of testing discrimination, id. at 425-26, except as to Hispanics who took Exam 8206; as to them a hearing was required, id. at 427. For Offerees who had not taken a test (and who therefore, the court reasoned, could only be victims of recruiting discrimination, if they were victims at all), the district court relied on Dr. Ashenfelter’s analysis that found a statistical imbalance between the expected and actual numbers of black, Hispanic, Asian, and female takers of the three challenged exams. Id. at 427-28. Having found manifest imbalances, the district court proceeded to the “unnecessary trammeling” stage of the inquiry. The district court found that the transfer and TCA effects of the Offerees’ retroactive seniority did not unnecessarily trammel the rights of the Brennan Plaintiffs, because race, national origin, or gender would rarely be the deciding factor in whether a Brennan Plaintiff got a transfer, and even when one of these was the deciding factor the Brennan Plaintiff remained eligible for future transfers. Id at 431. But the district court held that layoff seniority for non-victims of discrimination would unnecessarily trammel the Brennan Plaintiffs’ rights. Id. at 431-34. After resolving those Title VII issues, the district court examined the Equal Protection Clause of the Fourteenth Amendment, since the Brennan Plaintiffs had also attacked the settlement under 42 U.S.C. § 1983. For the minority male Offerees the district court applied strict scrutiny to the settlement grants of retroactive seniority. NYC Board III, 448 F.Supp.2d at 434-35. This meant the City Defendants had to show (1) a compelling interest for adopting the retroactive seniority, and (2) that the retroactive seniority was narrowly tailored to meet that interest. The district court said that, in this particular case, such a showing required the City Defendants to demonstrate a strong basis in evidence that the Board’s own tests and/or recruiting practices were discriminatory. The court then held that the required showing was satisfied for Black and Hispanic Offerees who failed a test, because the Board had created the exams and the tests were adequately shown to be discriminatory against those racial groups. It was not, however, satisfied for non-test-taking male Offerees because although there was a significant disparity between the number of white test-takers and the number of black, Hispanic, or Asian test-takers, there was no sufficient evidence that this disparity was caused by the Board’s own recruiting practices. Id. at 434-35. The district court rejected the Brennan Plaintiffs’ claim that a compelling interest always requires a showing of intentional disparate treatment by the governmental entity asserting the interest, for such a requirement was, in the district court’s judgment, inconsistent with Supreme Court precedent and the policy of encouraging settlement of Title VII cases. Id at 436-38. The court also found that the transfer and TCA seniority remedy for the test-failer Offerees was narrowly tailored under the factors listed in United States v. Paradise, 480 U.S. 149, 171, 107 S.Ct. 1053, 94 L.Ed.2d 203 (1987). Id at 438-40. Layoff seniority even for these Offerees, however, was not narrowly tailored. Id. at 440-41. For female Offerees, the analysis was different. The district court, applying intermediate scrutiny, did not require any showing of governmental (Board) involvement in the discrimination the Board sought to remedy, so the City Defendants’ interest in remedying gender discrimination could survive intermediate scrutiny even where their interest in remedying race discrimination might not survive strict scrutiny. Id. at 441-43. Having found that transfer and TCA seniority met the “narrowly tailored” standard during its strict scrutiny analysis, the district court easily determined that transfer and TCA seniority were “substantially related” for intermediate scrutiny purposes as well. Id. at 442-43. The district court concluded its first opinion by addressing two other matters. First, the court refused to enter, as a consent judgment, the parts of the settlement agreement that had survived the Brennan Plaintiffs’ Title VII and Equal Protection Clause attacks. Id. at 443-44. Second, the Brennan Plaintiffs had sought class certification with respect to their claims for declaratory and injunctive relief. Even though none of the other parties in either action had submitted responsive papers, the district court approved the class under Fed.R.Civ.P. 23. Id. at 444^16. The certified class consisted of “all custodial employees whose layoff-protection rights have been adversely affected by the grant of seniority benefits to beneficiaries who are non-victims of discrimination.” Id. at 446. The district court then listed the factual issues that still required a hearing: (a) which, if any, of the beneficiaries, in addition to Lloyd Bailey, Joseph Christie, Belfield Lashley, Gilbert Rivera, Peter Robertin, Felix Torres and Mayra Zephrini (Cintron), are actual victims of discrimination and received the relief to which they were entitled; (b) whether the results of Exam 8206 in respect to Luis Torres satisfy the evidentiary standards for establishing discrimination under Title VII and the Fourteenth Amendment; and (c) whether John Mitchell and Eric Schauer[, the plaintiffs seeking damages in the second consolidated action,] were denied transfers in favor of particular individuals who impermissibly received retroactivity [sic] seniority. Id. at 447-48. B. The April 20, 2007 Opinion After holding hearings on the remaining factual issues, the district court issued a second opinion. See NYC Board TV, 487 F.Supp.2d 220. This opinion discussed the results of those hearings and responded to several motions for reconsideration. In it the court held that: • Exam 8206 had been adequately shown to have had a disparate impact on Hispanics. Id. at 224-32. • There was an issue of fact requiring a hearing as to whether the parties to the 1999 settlement agreement intended to distinguish between “testing claimants” and “recruiting claimants,” or whether instead “the intent of the Agreement was to give relief to blacks and Hispanics regardless of whether they failed a challenged exam.” Id. at 232-33. • If the former were true, then the district court would not hold a hearing as to whether any recruiting-claim Offerees were actual victims of discrimination, because at summary judgment there was insufficient evidence to warrant a hearing on any claim that they were actual victims. Id. at 224 n. 3, 233-34. • If the latter were true, the district court said, it would be necessary to reconsider the Equal Protection Clause “narrow tailoring” analysis for the male recruiting claimants. Id. • As a clarification, the Equal Protection Clause prohibited not only contested retroactive seniority for the minority male recruiting claimants, but also seniority benefits based, under the settlement agreement, on these claimants’ permanent appointment dates. Id. at 234-35. • The Brennan Plaintiffs’ class was expanded to include “all custodial employees whose seniority for purposes of transfers, TCAs and layoff protection has been adversely affected by the grant of seniority benefits to the Offerees.” Id. at 236. In other words, the class was no longer limited to individuals affected by the grant of seniority benefits to non-victims of discrimination, nor was it limited to individuals who lost layoff protection rather than transfers or TCAs. C. The May 28, 2008 Opinion The third opinion was issued in May 2008 after a hearing on the intent of the parties to the 1999 settlement agreement. See NYC Board V, 556 F.Supp.2d 202. The court addressed two issues: first, whether the parties in 1999 intended to categorize Offerees into “testing-claim beneficiaries” and “recruiting-claim beneficiaries”; second, who among the testing-claim beneficiaries was an actual victim of testing discrimination. At the hearing, the district court heard the testimony of (1) Norma Cote, who had negotiated the settlement for the City Defendants, and (2) Katherine Baldwin, a Government lawyer who was not directly involved in the settlement negotiations but who reviewed and approved the agreement for DOJ policy compliance. Id. at 205-06. Cote testified that the Government had never separated the claimants into recruiting and testing beneficiaries, nor had it told the City Defendants that “the United States[] intended the settlement agreement to provide make-whole relief calibrated to each [OJfferee’s individual injury.” Id. at 205. Indeed, she testified that she did not recall the Government “ever explaining] to [her] why they wanted these individuals to get retroactive seniority.” Id. at 205-06. Baldwin testified that DOJ’s policy was “only [to] seek relief for identified victims of discrimination, [m]ake whole relief for identified victims of discrimination.” Id. at 206. Baldwin said that she and DOJ would not have approved the agreement if it had violated that policy. Id. Based on this testimony, the district court “conelude[d] that had the [City Defendants] and the United States operated under the assumption- — -now embodied in the Court’s holdings- — that there was a sufficient evidentiary basis only for testing discrimination, blacks and Hispanics who had not taken one of the challenged exams would not have been included in the list of Offerees.” Id. at 207. The district court noted that the parties must have been aware in 1999 that (1) some recruiting claimants were being given retroactive seniority, because Asians and non-Hispanic, non-black women received that relief, and (2) “some blacks and Hispanics had not taken one of the challenged exams because that factor was relevant in determining whether relief would be based on the median hire date for a challenged exam or provisional hire date.” Id. at 206-07. But the district court said that Baldwin’s testimony was “[m]ost compelling,” and that “[although the Court credits Cote’s testimony that the policy was not communicated to the Board, ... the United States simply would not have condoned any agreement that went beyond [make-whole] relief [to actual victims].” Id. at 207. The court also suggested that it was relying on “the general principle of contract law that ‘reformation may be available where the parties were under no mistake as to the words of the writing, but they supposed that the legal outcome would be different.’ ” Id. at 207 n. 4 (quoting 27 Williston on Contracts (4th ed.2003) § 70:128). For these reasons, the district court decided not to reconsider its holding that retroactive seniority for male recruiting claimants would not be “narrowly tailored” for Equal Protection Clause purposes. Id. at 207. The court then made determinations as to who among the 27 testing claimants were actual victims. The court said that, for each of these claimants, the question was “whether the retroactive seniority they received approximately corresponds to the seniority they would have received but for the discriminatory exams.” Id. at 209. Additionally, “the parties to the Agreement — i.e., the United States and the Board — bear the burden of proof.” Id. The court’s determinations were as follows: • Seven — Lloyd Bailey, Joseph Christie, Belfield Lashley, Gilbert Rivera, Peter Robertin, Felix Torres, and Mayla Zephrini (Citron) — were victims of discrimination who received appropriate make-whole relief, because the Brennan Plaintiffs had (supposedly) acknowledged this. Id. at 208 & n. 6. • Ten — the Arroyo Intervenors — did not require a determination as to actual victim status because they had stipulated to layoff seniority dates. Id. at 208 & n. 7. • Two, Ronald Johnson and Fidel Seara, did not require a determination because the former had retired and the latter had died. Id. at 208. • For the remaining eight, the parties had stipulated to facts but were unable to agree on their legal effect, so the court had to decide whether they were actual victims who had received make-whole relief. • Ricardo Cordero was an actual victim and received appropriate make-whole relief. He had failed Exam 5040, and his retroactive seniority date was appropriately the median hire date for that exam. Id. at 209. • Vernon Marshall was an actual victim, but his retroactive seniority date required adjustment because, “for reasons that are not clear,” it was over two years earlier than the median date for the exam he failed. Id. at 209-10. • Sean Rivera was not an actual victim. The settlement agreement had given him a retroactive seniority date of November 7, 1995. He scored an 80 on Exam 1074, which had a median hire date of October 27, 1997. This barely-passing score put Rivera close to the bottom of the Eligibility List for the exam, so that