Judge SACK concurs in part and dissents in part in a separate opinion.
JACOBS, Circuit Judge:In 1996, this Court affirmed findings by the United States District Court for the Southern District of New York (Sand, J.) that the State of New York had been aware of de jure segregation by the City of Yonkers in its public schools, and that the State failed to take corrective measures. See United States v. City of Yonkers, 96 F.3d 600, 611 (2d Cir.1996). At the same time, we held (reversing the district court) that the State could for that reason be liable under the Fourteenth Amendment or the Equal Education Opportunities Act, see id. at 619, 621, and remanded for further proceedings. The case now returns to us following the district court’s finding that the school system still labors under vestiges of de jure segregation, and entry of a judgment embodying a remedy supplemental to one imposed a decade earlier and intended (like the earlier remedy) to eradicate the vestiges of school segregation in Yonkers.
The order appealed from finds that two vestiges remain in the Yonkers schools: (i) low teacher expectations for minority students, and (ii) insufficiently multi-cultural orientation of teaching techniques and curriculum. The district court ordered the State to contribute $575 million over nine years to help fund various remedial measures.
The defendant State of New York (joined by the defendant City of Yonkers) contests the district court’s finding that vestiges of segregation remain in the school system. In opposition, the plaintiff National Association for the Advancement of Colored People (“NAACP”) argues that the findings are adequately supported by the evidence; on that issue, the NAACP is joined by the defendant Yonkers Board of Education, which would enjoy a large infusion of State funding if the order is af*306firmed and which reproaches itself for failing to obliterate segregation.
The State appeals on the further grounds (i) that the remedy imposed exceeded the district court’s authority; (ii) that the cross-claims filed against it by the Yonkers parties (the City and the Board) are barred by the doctrine of municipal incapacity; (iii) that the NAACP lacks standing to litigate the apportioning of liability among the defendants; and (iv) that the district court impermissibly assessed against the State half the annual cost of remedial measures. As to these issues, the City joins the NAACP and the Board in urging affirmance of the remedial orders.
In this opinion, we arrive at the following conclusions:
• Ordinarily, the parties seeking to end court supervision of schools bear the burden of persuasion on the issue of whether the school system is free of the vestiges of segregation. However, in the absence of findings that there are vestiges of segregation in student attendance, faculty, staff, transportation, extracurricular activities, and facilities— the so-called Green factors listed in Green v. County School Board, 391 U.S. 430, 435, 88 S.Ct. 1689, 1693, 20 L.Ed.2d 716 (1968) — the burden is properly placed on the parties that desire to prolong judicial oversight. In this case, therefore, the burden rests with the NAACP and with the Board of Education, the party that has best access to information relevant to the issue.
• The NAACP and the Board have failed to carry their burden of demonstrating that the two circumstances identified by the district court exist and are vestiges of prior segregation. The evidence supporting these findings was almost entirely anecdotal, and failed to forge an adequate causal link between the regime of de jure segregation and any ongoing remediable deficiency. Likewise, statistical evidence about racial disparities in educational achievement failed to demonstrate that the racial gap was the product of prior segregation, as opposed to, for example, ambient societal racism.
• The remedy imposed by the district court exceeded its broad remedial authority because the remedy constitutes by and large a general school improvement program. The court failed to articulate the required nexus between any ongoing injury caused by unconstitutional conduct and proposed remedial measures.
• As the case is currently structured, we reject the State’s arguments on municipal incapacity and standing. Since the State concedes that the NAACP plaintiffs do have standing to litigate the State’s liability and the scope of the remedy, the district court has little choice but to apportion costs among the joint tortfeasors.
• Finally, the district court did not exceed its remedial authority in allocating to the State one-half the annual costs of its previously-imposed remedy. At the same time, we leave it to the district court on remand to assess the ongoing efficacy and necessity of that remedy.
BACKGROUND
We will assume familiarity with our previous decisions in the case, see United States v. City of Yonkers, 96 F.3d 600 (2d Cir.1996) (“Yonkers V”); United States v. Yonkers Bd. of Educ., 837 F.2d 1181 (2d Cir.1987) (“Yonkers III”), and will here emphasize only those facts and circumstances that bear upon the issues presented on this appeal.
In 1980, the United States sued the City of Yonkers, the Yonkers Board of Education, and the Yonkers Community Development agency, alleging housing and school segregation in violation of the Equal Protection Clause and federal civil rights statutes. The NAACP intervened as a plaintiff the following year, and the case *307was subsequently certified as a class action.
After trial, the district court found that the defendants had committed intentional racial discrimination in housing and in education. See United States v. Yonkers Bd. of Educ., 624 F.Supp. 1276 (S.D.N.Y.1985) (Sand, J.) (“Yonkers I”). Specifically, the Board had clung to a neighborhood school policy with full knowledge that its location of subsidized public housing in poorer neighborhoods of the City would be conducive to segregated schools; had manipulated school openings and closings and attendance zones to create and preserve racially identifiable schools; had rejected several reasonable proposals that would have desegregated the student population; had consigned students in predominantly minority schools to inferior facilities and staff; had followed a policy of disproportionately assigning minority teachers and staff to schools with predominately minority student populations; and had assigned minority students disproportionately to special education classes. See Yonkers III, 837 F.2d at 1212-14. The district court found that the City was also liable for school segregation because it had pursued a discriminatory housing policy with the intent (in part) to keep racially identifiable schools, and because the mayor’s appointments to the Board of Education evinced a desire to continue segregated schools in Yonkers. See id. at 1214-15.
A year later, the district court issued its remedial order for the Yonkers schools. See United States v. Yonkers Bd. of Educ., 635 F.Supp. 1538 (S.D.NY.1986) (Sand, J.) (“Yonkers II”). Its stated goal was to achieve the desegregation of the student population in every school in the system by the 1987-88 school year.1 The principal tools for achieving that goal were the creation of City-funded magnet programs to attract non-minorities to predominately minority schools and the adoption of a “controlled choice” system for student assignments. See Yonkers III, 837 F.2d at 1215. This remedial order has come to be known as the first Educational Improvement Plan (“EIP I”).
We affirmed Yonkers I and Yonkers II in 1987. See id. at 1239.
Under EIP I, the Yonkers schools achieved “enrollment” desegregation during the 1986-87 school year and did so “in a relatively smooth and peaceful manner.” United States v. City of Yonkers, 833 F.Supp. 214, 216 (S.D.N.Y.1993) (Sand, J.) (“ Yonkers IV").
In September 1987, the Board of Education sought leave to file a cross claim against the State and numerous state agencies and employees, and the NAACP moved to amend its complaint to name as defendants the same State parties. At roughly the same time, and at the district court’s invitation, the Board began formulating a second Educational Improvement Plan (“EIP II”).
The state defendants’ motions to dismiss and for summary judgment were denied in 1989 and 1992, respectively. See United States v. City of Yonkers, No. 80 CIV. 6761(LBS), 1989 WL 88698 (S.D.N.Y. Aug.1, 1989), appeal dismissed, 893 F.2d 498 (2d Cir.1990); United States v. City of Yonkers, No. 80 CIV. 6761(LBS), 1992 WL 176953 (S.D.N.Y. July 10, 1992). The district court then ordered a trifurcated trial to establish: (1) whether “vestiges” of segregation remained in the Yonkers schools despite EIP I; (2) whether there was a causal relationship between any unconstitutional actions by the State defendants and those vestiges; and (3) what remedy, if any, would be appropriate.
*308After the first phase of this three-part proceeding, the district court held that vestiges of segregation persisted. Although the district court placed considerable weight on racial disparities in achievement test results, it treated the testing disparities as evidence of vestiges but declined to consider them vestiges of segregation in themselves. See Yonkers IV, 833 F.Supp. at 222. The court relied on a study prepared by a Board expert that applied multiple regression analysis to students’ reading and math scores on the Metropolitan Achievement Test. The study concluded that race was a statistically significant factor in accounting for disparities in performance even after controlling for other possible influences, such as placement in special education, poverty (for which receipt of subsidized lunches was used as a proxy), attendance at schools where many students receive subsidized lunches, and limited English language skills. See id. at 221. The district court acknowledged that the study “suffered] from a lack of adequate base data” and that there could be other factors contributing to the disparity in results, such as weight at birth, the educational level of parents, and living in a single-parent household. Id. at 221-22. The court did not credit evidence adduced by the State (i) that other urban school districts nationally suffered from the same racial gaps in achievement scores, see id. at 223 (“[T]he widespread nature of the problem ... does not provide an excuse for inaction.”); (ii) that the lack of adequate multi-cultural training was attributable to the staffs “intransigence” rather than a lack of funds, id.; and (iii) that ongoing disparities in educational results are attributable to intervening demographic changes rather than to historical segregation, see id. at 224-25.
Beginning with “the premise that all children can learn,” Judge Sand found that the Board of Education had demonstrated that the test disparities resulted from vestiges of discrimination, and identified two ongoing circumstances as vestiges of segregation resulting in racial disparities in educational quality: (i) low teacher expectations for minority students and (ii) insufficiently multi-cultural curricula and teaching techniques. See id. at 222-23.
The State did not appeal • the district court’s 1993 decision on vestiges because it was the first stage of a trifurcated trial. Although this Court’s 1996 opinion ruled on other aspects of the case, it noted that the finding of vestiges was not under review. See Yonkers V, 96 F.3d at 604. That matter therefore comes before this Court for the first time in this appeal.
The second phase of the trifurcated litigation is not directly relevant to this appeal. After a trial in 1995, the district court found as facts that the State knew or should have known of the de jure segregation in the Yonkers public schools and that it had failed to take action to end it. See id. at 604-05. As a matter of law, however, the district court held that the State’s omissions could not be the basis of liability for violation of the Fourteenth Amendment or of the Equal Educational Opportunities Act of 1974 (“EEOA”), 20 U.S.C. §§ 1701-1758. In 1996, this Court affirmed the district court’s factual findings on the State’s acts and omissions but reversed its legal holding, and thereby opened the door to State liability. See Yonkers V, 96 F.3d at 611.
With this Court’s reinstatement of the case against the State, the district court proceeded in 1997 to the remedial (and final) phase of the trifurcated trial. Four years had passed since the district court’s 1993 vestiges ruling, so the court wisely took the opportunity to revisit the question of whether vestiges of segregation persisted.
At trial in 1997, the State offered evidence showing that the achievement disparities in Yonkers were comparable to those in four other New York school districts that had similar demographics but had never been found to have practiced de jure segregation. See United States v. *309Yonkers Bd. of Educ., 984 F.Supp. 687, 690 (S.D.N.Y.1997) (Sand, J.) (“Yonkers VI”). The Board of Education countered with (i) an updated version of its 1993 regression analysis; (ii) evidence of disparities in dropout rates, suspension rates, and rates of assignment to special education classes; and (iii) anecdotal evidence that some Yonkers teachers have low expectations for minority students. See id.
The Court rejected the State’s data comparing test-score disparities in Yonkers with disparities in comparable districts in the State, noting that those districts could also be suffering from the vestiges of prior discrimination, whether or not de jure segregation had been judicially found. See id. at 690-91. Without extended discussion, the court “adopt[ed] and reaffirm[ed]” its 1993 vestiges decision. Id. at 691.
In the same 1997 decision, the court found that although EIP I had achieved numerical integration of the Yonkers schools, EIP I was insufficient to remedy perceived disparities in education afforded minority students. See id. at 691, 694-95. It therefore adopted a set of measures developed by the Yonkers Board of Education, and designated EIP II. See id. at 698-99. Those measures, outlined in broad terms in the district court’s order, see id. at 713-24, and subject to further refinement, include the following:
• Implementation of State and national curricular standards, in addition to support services and “skills programs” to enable students to succeed in demanding courses.
• Recruitment and training to better enable staff to teach a diverse student body.
• “Information rich classrooms,” including networked computers and improved libraries.
• Full-day pre-kindergarten.
• Smaller classes (to be accomplished by hiring more teachers) and smaller school size.
• Improved and expanded educational programs tailored to students for ■ whom English is a second language.
• Programs intended to increase parental involvement in the schools.
See id. at 714-21.
With this end to the trifurcated trial, the district court’s judgment became final and appealable. On appeal, the State argues that (1) the evidence of vestiges of prior segregation was legally insufficient; (2) the remedy imposed by the district court was inappropriate; (3) the claims against it should be dismissed on the grounds of municipal incapacity and lack of standing; (4) the district court erred in allocating to the State half the costs of EIP I. The City supports the State in its first ground of appeal but opposes the State on all other' issues. The NAACP and the Board of Education oppose all of the State’s arguments.
DISCUSSION
A. Vestiges
1. Standard of Review
We review a district court’s findings of fact in a desegregation case for clear error. See Fed.R.Civ.P. 52(a); Freeman v. Pitts, 503 U.S. 467, 474, 112 S.Ct. 1430, 1437, 118 L.Ed.2d 108 (1992). A district court’s conclusion that there are legally sufficient vestiges of segregation in a school district, however, is a mixed question of law and fact. As such, we subject it to de novo review. See Lopresti v. Terwilliger, 126 F.3d 34, 39 (2d Cir.1997).
2. Burden of Persuasion
A preliminary question is: Who bears the burden of persuasion on the issue of whether vestiges of segregation remain in the Yonkers schools? In a case dealing with the desegregation of higher education, the Supreme Court ruled that “the burden of proof falls on the State, and not the aggrieved plaintiffs, to establish that it has dismantled its prior de jure *310segregated system.” United States v. Fordice, 505 U.S. 717, 739, 112 S.Ct. 2727, 2741, 120 L.Ed.2d 575 (1992). In this case, however, the dismantling of the de jure system of segregated schools has been accomplished with respect to all of the Green factors, and the issue is whether the district court has identified other ills of the school system that are traceable to historical segregation. Our analysis of traditional principles of burden allocation, and of the facts and circumstances of this case, convinces us that plaintiffs, not the State, bear this burden of persuasion. Cf. Coalition to Save Our Children v. State Bd. of Educ., 90 F.3d 752, 776-77 (3d Cir.1996) (plaintiffs bore burden of proving causal link between segregation and achievement gap in the absence of Green factors or violations of previous remedial orders); School Bd. v. Baliles, 829 F.2d 1308, 1311-13 (4th Cir.1987) (plaintiffs bore burden when district achieved “unitary” status on all Green factors).
In civil litigation, there are no clear, dispositive rules for allocating the burden of persuasion, which often is “merely a question of policy and fairness based on experience in the different situations.” 9 John Henry Wigmore, Evidence § 2486, at 291 (Chadbourn rev.1981).
A general principle, subject to numerous exceptions, is that the party seeking to change the status quo bears the burden of persuasion on every element of the cause of action. See Edward W. Cleary, Presuming and Pleading: An Essay on Juristic Immaturity, 12 Stan. L.Rev. 5, 7 (1959). This general principle yields no easy answer in an equitable case such as this. The plaintiffs here are seeking to change the status quo by remedial measures that they seek to continue and enhance, while the State seeks to change the status quo by ending or narrowing the long judicial oversight of the Yonkers schools.
" The commentators discuss three principles that guide the allocation of burdens in specific situations: fairness, policy, and probability. See id. at 11-14.
Fairness militates in favor of placing the burden on the party with the readiest access to information on the contested issue. See Fleming James, Jr., et al. Civil Procedure § 7.16, at 344 (4th ed.1992). This rationale is less than compelling in the era of liberal discovery, and is honeycombed by exceptions. See, e.g., Richard A. Epstein, Pleadings and Presumptions, 40 U.Chi.L.Rev. 556, 581-82 (1973) (pointing out that burden of proving negligence remains on plaintiff despite defendant’s easy access to information on the issue). To the extent this principle should operate in the ordinary context of desegregation litigation, it argues for placing the burden of proving the lack of vestiges of segregation on the school boards and municipalities as entities having superior access to information, especially information about their own motivation and performance.
The case before us is atypical in that the party with the best access to information on the contested issue of vestiges, the Yonkers Board of Education, though a nominal defendant, is vigorously arguing that vestiges of discrimination persist in the school system it administers, and the Board has a compelling financial incentive to depict its school system in the most dismal light.
In policy terms, a party that has been found to have implemented de jure segregation should ordinarily bear the burden of demonstrating that the vestiges of its prior wrong have been eradicated. At the same time, the Supreme Court has emphasized that desegregation suits implicate another imperative as well:, returning control of schools to local authorities. See Missouri v. Jenkins, 515 U.S. 70, 88-89, 102, 115 S.Ct. 2038, 2049, 2056, 132 L.Ed.2d 63 (1995). Where racial disparity persists in one of the quantifiable factors identified in Green — student enrollment, faculty, staff, transportation, extracurricular activities, and facilities — the value of *311local control should not affect the calculus on the risk of non-persuasion. For example, a school district that once practiced de jure segregation and still has racially identifiable schools must shoulder the burden of proving that the state of affairs is not a vestige of segregation.
The analysis is necessarily different where (as here) all parties agree there are no vestiges of segregation in any of the Green factors. Cf. Swann v. CharlotteMecklenburg Bd. of Educ., 402 U.S. 1, 18, 91 S.Ct. 1267, 1277, 28 L.Ed.2d 554 (1971) (concluding that “existing policy and practice with regard to [the Green factors are] among the most important indicia of a segregated system”); Coalition to Save Our Children, 90 F.3d at 776-77 (“Because the performance disparities claimed by [the plaintiff] are not among (or even similar to) the Green factors ... we will not simply presume ... that these are vestiges of de jure segregation.”); Daniel J. McMullen & Irene Hirata McMullen, 44 Case W.Res.L.Rev. 75, 107 (1993) (“Obviously, the presumption most readily applies to those factors most directly affecting or manifesting the racial identifiability of schools — i.e., student and faculty assignments .... ”). Where the residual effects of segregation are not grounded in any of the Given factors, the return of school control to local authorities militates more strongly in favor of placing the burden of persuasion on those who argue that racial differences in achievement are caused by segregation.
The burden-allocation analysis is informed by a third principle, probability, which tends to place the burden of proving a proposition on the party whose version of events is atypical in judicial experience. In the context of school desegregation, courts often conclude that once there has been an initial finding of de jure segregation, it is highly probable that other conditions with segregative effect are also caused by de jure segregation. See Keyes v. School Dist. No. 1, 413 U.S. 189, 207-08, 93 S.Ct. 2686, 2697, 37 L.Ed.2d 548 (1973); see also Note, Allocating the Burden of Proof After a Finding of Unitariness in School Desegregation Litigation, 100 Harv.L.Rev. 653, 657-60 (1987).
However, in Yonkers, there is no school segregation today. All parties agree that there is no racial identification in student population, in faculty assignment, or in other areas. The putative disparity is in the quality of education for minority and non-minority children, as deduced from differences in results in achievement testing.
Judicial experience suggests that racial disparities in the Given factors often result from segregation or its vestiges, and the burden falls on the person arguing that such a disparity is not a vestige of segregation. We discern no comparable judicial experience with disparities in “quality of education,” at least absent a colorable claim of residual segregation measurable by a Green factor. There is no basis in experience or intuition for saying that in the general run of cases, racial achievement gaps in a school district are a lingering result of a regime of de jure segregation that is historically remote (as measured by the age of schoolchildren). Therefore, the probabilities of this case do not support placing on the State the burden of proving a lack of vestiges of segregation.
In sum, this is an unusual school desegregation case, with a counterintuitive alignment of parties, strong incentives for self-accusation, an absence of vestiges detectable by any of the Green factors, vexed questions of causation, and a dearth of comparable litigation from which to make reasonable assessments of probabilities. In these circumstances, we hold that the burden of proving vestiges of segregation falls upon the parties contending that such vestiges exist. As we said at the outset of this section, sister circuits in somewhat analogous cases have arrived at the same conclusion. See Coalition to Save Our *312Children, 90 F.3d at 776-77; School Bd. v. Baliles, 829 F.2d 1308, 1311-13 (4th Cir.1987).
S. Vestiges
Since the Supreme Court’s opinion in Green, courts have repeatedly held that the removal of official impediments to student integration is not a complete remedy for de jure segregation in schools. “[A] state does not discharge its constitutional obligations until it eradicates policies and practices traceable to its prior de jure dual system that continue to foster segregation.” United States v. Fordice, 505 U.S. 717, 728, 112 S.Ct. 2727, 2735, 120 L.Ed.2d 575 (1992). It need not be shown that such vestiges have a discriminatory purpose, only that they have a discriminatory effect. See id. at 732-33 & n. 8, 112 S.Ct. at 2738 & n. 8.
To recapitulate, the Green court listed six areas in which school districts were required to end racial disparities: student enrollment, faculty, staff, transportation, extracurricular activities, and facilities. See Green v. County School Board, 391 U.S. 430, 435, 88 S.Ct. 1689, 1693, 20 L.Ed.2d 716 (1968); Swann, 402 U.S. at 18, 91 S.Ct. at 1277. These Gi-een factors are not necessarily the only measures of residual segregative effect, see Freeman v. Pitts, 503 U.S. 467, 493, 112 S.Ct. 1430, 1446, 118 L.Ed.2d 108 (1992), but they are “among the most important indicia of a segregated system,” Swann, 402 U.S. at 18, 91 S.Ct. at 1277.
It is undisputed that the Yonkers School Board has achieved full integration as measured by the Green factors. The issue now is whether the school system dis-serves its minority students by delivering the same instruction to all its pupils, and by having some teachers who expect minority children to do less well when so instructed. These quality-of-education factors are not among the indicia listed in Green, but other courts have considered quality of education in assessing whether a school system has fully overcome its history of segregation. See, e.g., Freeman, 503 U.S. at 492-93, 112 S.Ct. at 1446. We will assume without deciding that disparities in quality of education alone may constitute a vestige of prior segregation. Cf. Wessmann v. Gittens, 160 F.3d 790, 801 (1st Cir.1998).
Before turning to the vestiges identified by the district court, we canvass a number of putative vestiges that are advanced by the Board to support the district court’s judgment, but that were not found by the district court.
The Board accuses itself of “within-school segregation.” Br. of Appellee Yonkers Bd. of Educ. at 37-39. Specifically, the Board confesses that its employees engage in race-conscious tracking of minority students into less challenging courses, and even segregate students within classrooms. See id. If true, these conditions would be alarming.2 But the district court did not find such practices, or deem within-school racial groupings to be a vestige of prior de jure segregation.
The Board also cited inadequate facilities, but Judge Sand could find “little or no correlation between the adequacy of a particular school facility and its prior racial identification.” Yonkers IV, 833 F.Supp. 214, 223 (S.D.N.Y.1993).
The district court referenced the Board’s self-indictment on a number of additional scores, including “the self-esteem and attitudes of students,” “the relationships between majority and minority students,” and “community perceptions concerning the Yonkers schools.” Id. at *313217. These subjects are not part of our review because the court made no findings on these subjects, and did not treat them as vestiges of segregation. See id. at 222-23.
The district court’s findings of vestiges of segregation in Yonkers are vague, but we perceive two relevant findings of racial disparity, both of which concern the quality of education: low teacher expectations for minority students, and an insufficiently multi-cultural approach to curriculum and teaching techniques. See id. at 222. As the district court acknowledged, the evidence on these matters was “largely anecdotal.” Id. The court’s opinion accords great weight and influence to racial differences in test scores. Although the court ultimately concluded that the disparities themselves are not vestiges of segregation, the testing differences are treated in the opinion as tantamount to vestiges. In this section, we examine in turn the two supposed vestiges and then consider the test score disparity.
(a) Educational Theory
Evidence that Yonkers’ curriculum and teaching techniques are insufficiently multi-cultural is legally insufficient to constitute a vestige of segregation. Our review is somewhat hampered by the district court’s failure to make specific factual findings on the subject, but because we do not want to prolong unnecessarily this already-lengthy litigation, we look to the record ourselves (and specifically to passages highlighted by the Board) rather than remand the case for a further articulation of findings.3 See Wessmann, 160 F.3d at 802.
Dr. Donald Batista, superintendent of the Yonkers public schools, testified that “most” of the teachers in the Yonkers schools were “trained in a segregated system.” As a result, “[t]hey are accustomed to ability grouping and dealing with homogeneous classes, and in many respects, they have not been trained to work with more heterogeneous classes, trained in understanding cultural diversity and multicultural education.”
AnneMarie Ciaramella, director of school improvement in the Yonkers Department of Administration, testified that many Yonkers teachers relied on traditional lecture techniques and were unfamiliar *314with “cooperative learning” (students learning together in small groups), which technique, she testified, is especially suited to the learning needs of minority students.
Edda Cardona-Zuckerman, a Yonkers principal, testified that teachers who started in the segregated system “were not prepared [and] were a bit overwhelmed” when the ending of segregation dramatically altered the racial and ethnic makeup of their classes. In the same vein, Betsey Hardeman, who was deputy superintendent of schools in Yonkers for two-and-a-half years, noted that “the teaching techniques have changed from when [older teachers] started to teach.” She expanded, “there was no cooperative learning back in those days ... there was not the amount of individualization, there was much more emphasis placed on lecture, there was much more emphasis placed on the teacher as directing the learning as opposed to teaching students to direct their own learning.”
For several reasons, this and other testimony does not furnish an evidentiary basis for a finding of a vestige of prior discrimination.
First, insofar as the testimony depicts the veteran teachers of the segregation era struggling unsuccessfully to cope with a changing student population, it fails to trace their presumed inadequacies to the practices and influences of segregation. For reasons unrelated to segregation or desegregation, the Yonkers school system has undergone dramatic demographic change over the course of this litigation. In 1985, 47% of the student population was black or Hispanic. By 1996, the figure was 71%, and the total student population had grown from under 19,000 to over 23,-000. Much of the growth in the minority population was attributable to immigration from Latin America. Assuming that distinct educational strategies are needed to teach children of differing ethnicity and race, the evidence cited by the Board demonstrates that the veteran teachers would have been challenged professionally by the same transitions in teaching methods and theories even if Yonkers had never imposed segregation. Cf. Missouri v. Jenkins, 515 U.S. 70, 102, 115 S.Ct. 2038, 2055-56, 132 L.Ed.2d 63 (1995); Pasadena City Bd. of Educ. v. Spangler, 427 U.S. 424, 434-36, 96 S.Ct. 2697, 2704, 49 L.Ed.2d 599 (1976).
Second, the Board of Education never adequately explains how any deficiencies in multi-cultural teaching techniques on the part of younger teachers could be fairly traced to the era of de jure segregation— before they started teaching. It is possible that these relatively new teachers received inadequate training, or that the Board is recruiting poor teachers, but neither state of affairs would constitute a vestige of prior segregation. It is not enough to suggest that new teachers are infected by their hidebound colleagues, and therefore cannot master new techniques. See Wessmann, 160 F.3d at 807 (“While the idea of ‘socialization’ may be intellectually elegant, courts must insist on seeing concrete evidence.”).
Third, pedagogical currents shift over time. It cannot be expected that every school district will succeed in continuously retraining its teachers, new and old, to be adept in current techniques. Failure to succeed at such an endeavor can be attributed to many things, but the linkage to long-ended segregation does not hold. The inability or unwillingness of some teachers to pursue strategies such as cooperative learning does not render the school system a constitutional violator. Cooperative learning did not even exist as a methodology when this litigation began, as Hardeman testified.
Fourth, curriculum is a sensitive matter, drawing subjective inputs from education policy, local politics and parental preference. Absent some extraordinary showing, we will not conclude that the Constitution requires a local school board to adopt one curriculum over another, or that children of differing ethnicity and race *315require separate curricula or teaching techniques. There was no demonstration that those who drafted the curriculum in 1980 acted with racial animus to craft a school program such that children of certain ethnicities or races would fail to learn, or that the curriculum represented anything other than the pedagogical thinking of the time. To cast the curriculum as a vestige of segregation, plaintiffs must show more than that it was adopted in the time of segregation and has since become outmoded. Plaintiffs have failed to show the causal link between de jure segregation and the purported yestige.
(b) Low Expectations
The district court did not cite specific facts or anecdotes to support its conclusion that low teacher expectations for minority students constitute a vestige of prior segregation. But the Board’s brief on appeal cites several examples, some of which we summarize below.
Jacquilynn Beville, a social worker employed by the Yonkers public schools, testified that in some schools teachers viewed minority students as “deficient because of either coming from another country, being bilingual, or coming from an urban or a poor neighborhood.” She also described “a tendency not to see [minority students’] potential for success” but rather to see “their weaknesses ... 'and to focus on that, and to teach to that level of performance.”
Sylvia A. Muckelvaney, a teacher and “multi-cultural liaison” at a magnet elementary school, said that she had “heard some teachers over the years make the statement that they don’t believe that all children can learn and in general they were referring at the time to children of color.” She also testified that when visiting colleagues’ classrooms to pick up something or have brief conversations, she has “noticed particular things that sort of make you look twice” about the teachers’ treatment of minority students.
Hardeman, the former deputy superintendent, observed on “several occasions” a minority student raising his or her hand to answer a question and “the teacher would say, you know, Johnny, put your hand down, you really don’t know the answer to that question.”
The district court opinion does not describe the causal link between these present-day low expectations and the pre-1986 era of de jure segregation. We have reviewed the evidence cited by the Board in support of the proposition that a causal link exists. A few representative examples follow:
Cardona-Zuckerman, a principal, testified that some of the teachers who had been in school system before 1986 “had gotten used to a particular population of children, children who were certainly in the mainstream, who didn’t have the degree of problems academically that the rest of the children who later on came in had.” Hardeman noted that the demographics of the Yonkers school population had changed dramatically during the tenure of some veteran teachers, and “[t]hey are not prepared to deal with that.”
The following exchange took place during examination of Dr. Gladys Pack, a Yonkers administrator:
[Pack]: ... [T]he vestiges [are] systemic in nature so that a new teacher coming in without that kind of training with the rest of the teachers and without the changes that need to be made is somewhat—
[Counsel]: You view it as a virus, that a new teacher coming in would automatically be affected but the teachers who have been there a long time are you assume to be infected?
[Pack]: I think it’s a system that is infected. Is it a kind of virus? Yes.
As these passages illustrate, the evidence that teachers have low expectations of minority students is entirely based on scattered anecdotes, and the evidence supporting a causal link between these low expectations and prior de jure segregation *316is a set of subjective, intuitive impressions. This is not enough. “The vestiges of segregation that are the concern of the law in a school case may be subtle and intangible but nonetheless they must be so real that they have a causal link to the de jure violation being remedied.” Freeman v. Pitts, 503 U.S. 467, 496, 112 S.Ct. 1430, 1448, 118 L.Ed.2d 108 (1992) (emphasis added); see also Board of Educ. v. Dowell, 498 U.S. 237, 246, 111 S.Ct. 630, 636, 112 L.Ed.2d 715 (1991) (vestiges must be described with sufficient precision so that defendants can have “a rather precise statement of [their] obligations”).
The First Circuit recently came to the same conclusion in a case challenging the use of race for admissions to the Boston Latin School. See Wessmann v. Gittens, 160 F.3d 790 (1st Cir.1998). The court concluded that anecdotes of low teacher expectations for minority students are legally insufficient to justify the challenged policy. See id. at 806 (“[AJnecdotal evidence alone can establish institutional discrimination only in the most exceptional circumstances.”). In particular, the court criticized the anecdotal evidence as failing to provide any quantitative proof of the pervasiveness of the purported problem, see id. at 806-07; this critique is equally valid in this case (assuming of course that one can quantitatively measure the inaccuracy of teachers’ expectations).
It is instructive to consider together the two findings of vestigial segregation made by the district court. The residual effects of segregation are said to be revealed on the one hand by low teacher expectations, and on the other hand by the failure to adopt teaching techniques targeted to minority children. Ciaramella, the director of school improvement, explained that traditional pedagogical approaches (such as lecturing) are inevitably targeted to the middle range of academic ability in a class. Given the “achievement gap” between minority and non-minority children, she said, that means that many minority children’s “ability to comprehend, understand and use information is not going to be met at all.” It is impossible to see how all vestiges of segregation can be erased if it is contended one vestige is low teacher expectations and the other is the failure of teachers to realize that minority students — presumed to be at the bottom of the class — are not reached by teaching techniques targeted to the middle. The more one adopts teaching techniques that assume minority students are at the bottom, the more one reinforces the idea of low expectations. This reciprocal effect would assure that the taint of segregation could never be purged. And it is clear enough that the Board has no incentive to rid itself of that taint so long as its self-accusation generates a flow of state remedial funds through this litigation.
(c) Test Scores
The district court found the regression analysis on racial disparities in achievement test scores (introduced at the 1993 vestiges trial) to be highly significant. Although the court expressly declined to consider the disparities as vestiges in themselves, it deemed them “consequences” of vestiges, see Yonkers TV, 833 F.Supp. 214, 222 (S.D.N.Y.1993), and placed heavy emphasis on them. Thus, the court observed that the Board’s “burden of showing that these achievement disparities result from vestiges of segregation is not a heavy one.” Id. (footnote omitted).
As other courts have recognized, using achievement test scores as a measure, either direct or indirect, of a school system’s movement away from segregation is deeply problematic. See, e.g., Missouri v. Jenkins, 515 U.S. 70, 101, 115 S.Ct. 2038, 2055, 132 L.Ed.2d 63 (1995); People Who Care v. Rockford Bd. of Educ., 111 F.3d 528, 537 (7th Cir.1997); Coalition to Save Our Children v. State Bd. of Educ., 90 F.3d 752, 776-78 (3d Cir.1996). True, the study examining test results in Yonkers was more sophisticated than studies that some other appellate courts have found insufficient. In an effort to isolate *317race as an explanatory factor, the study controlled for some other possible factors, including enrollment in special education, level of English ability, prior test scores, receipt of subsidized or free lunch (a crude proxy for socio-economic status), and attendance at schools with a high concentration of children receiving a subsidized or free lunch. See Yonkers IV, 833 F.Supp. at 221. As the district court acknowledged, however, the study failed to control for several other factors that could explain some or all of the gap, including “birth weight, educational and occupational background of parents, parental interest and involvement, single parent status, ... mobility and other socio-economic factors.” Id. at 222. Without taking account of such factors, which describe profound childhood influences, the study’s conclusion that there is a purely racial achievement gap in Yonkers strikes us as result-driven. Cf Wessmann, 160 F.3d at 802 (“[W]hether past discrimination necessitates current action is a fact-sensitive inquiry, and courts must pay careful attention to competing explanations for current realities.”).
The district court nevertheless chose to credit the study’s conclusion, and we need not decide whether that reliance was clear error, because there is a deeper problem with the use of the study. The study itself shows only differential achievement levels by race; it does not purport to take the next step and give reasons for that gap. Accepting arguendo the study’s conclusion of a racial disparity, the study fails to show that the disparity-was caused by pre-1986 segregation in Yonkers, as opposed to, for example, generalized “societal discrimination.” Wessmann, 160 F.3d at 803-04; see also Swann v. Charlotte-Mecklenburg Bd. of Educ., 402 U.S. 1, 22, 91 S.Ct. 1267, 1279, 28 L.Ed.2d 554 (1971) (“The elimination of racial discrimination in public schools is a large task and one that should not be retarded by efforts to achieve broader purposes lying beyond the jurisdiction of school authorities. One vehicle can carry only a limited amount of baggage.”).
The State introduced unrefuted evidence at the 1997 trial showing that the racial disparities in Yonkers were no greater (and in many instances smaller) than those present in comparable New York school districts, districts in which there has never been a finding of de jure segregation. The district court rejected those comparisons on the ground that de jure segregation may have existed in the control districts even if it escaped adjudication. See Yonkers VI, 984 F.Supp. 687, 690-91 (S.D.N.Y.1997). That is of course possible. But the district court’s approach would invalidate reality-checking comparisons with any and all other districts. The burden of proof comes into play at this juncture. If (as is the case) the Yonkers Board cannot demonstrate salient differences between its experience with changing school demographics and the experience of other school districts, there is no reason to attribute the Yonkers experience to circumstances particular to Yonkers and its history of segregation.
In short, a finding of prior segregation, coupled with a finding of present day racial differences in educational achievement, is an insufficient positive test for the presence of residual segregative effects. See Wessmann, 160 F.3d at 801.
B. Remedy
The Supreme Court has listed three principles that guide a court’s exercise of remedial powers in a school desegregation case. First, “the nature of the desegregation remedy is to be determined by the nature and scope of the constitutional violation.” Milliken v. Bradley, 433 U.S. 267, 280, 97 S.Ct. 2749, 2757, 53 L.Ed.2d 745 (1977); see also Yonkers III, 837 F.2d 1181, 1235 (2d Cir.1987) (“[T]he court should tailor- the remedy to fit the nature and extent of the violation.”). Second, the desegregation decree “must indeed be remedial in nature, that is, it must be designed as nearly as possible ‘to re*318store the victims of discriminatory conduct to the position they would have occupied in the absence of such conduct.’ ” Milliken, 433 U.S. at 280, 97 S.Ct. at 2757 (quoting Milliken v. Bradley, 418 U.S. 717, 746, 94 S.Ct. 3112, 3128, 41 L.Ed.2d 1069 (1974)). Finally, the court “must take into account the interests of state and local authorities in managing their own affairs, consistent with the Constitution.” Id. at 280-81, 97 S.Ct. at 2757.
To satisfy the last of these three principles of discretion requires that any remedial order contemplate “limits to the duration of the District Court’s involvement.” Jenkins, 515 U.S. at 99, 115 S.Ct. at 2054. An open-ended remedial regime, in combination with a potentially collusive alignment of parties, can create a troubling dynamic:
Each additional program ordered by the District Court — and financed by the State — ■... makes the [local school district] more and more dependent on additional funding from the State; in turn, the greater the [district’s] dependence on state funding, the greater its reliance on continued supervision by the District Court.
Id. This incentive effect runs counter to the “vital national tradition” of autonomous local school districts and to the directive that a “district court must strive to restore state and local authorities to the control of a school system operating in compliance with the Constitution.” Id.
We need not conduct an exhaustive review of the EIP II remedy ordered by the district court in this case; it will doubtless be revisited in light of our reversal on the finding of vestiges. Moreover, since we have found that the record presents insufficient evidence of ány constitutional violation or vestige of a previous violation, we cannot assess whether the remedy is correctly tailored. But the open-ended nature of the remedy imposed here reinforces our conclusion that the existence of vestiges of segregation has been inadequately demonstrated. Maybe EIP II includes valuable educational components and effectively remedies the ills of the school system; maybe it does not. But there has been no adequate showing that it is responsive to the only ill that counts for purposes of this litigation: de jure segregation and its after-effects. Measures such as networked computers in classrooms and full-day pre-kindergarten are more properly characterized as general educational enrichments rather than remedies for prior segregation. See Swann, 402 U.S. at 16, 91 S.Ct. at 1276 (“Remedial judicial authority does not put judges automatically in the shoes of school authorities whose powers are plenary. Judicial authority enters only when local authority defaults.”). Desegregation remedies that include enhanced funding may yield incidental benefits, enrichments and amenities. But the animating purpose of desegregation remedies must always be to put the victims of constitutional injury where they would have been but for the injury. See MiUiken, 433 U.S. at 280, 97 S.Ct. at 2757. Absent a focused identification by the district court of what vestiges of segregation persist in Yonkers, and an explanation of how each individual remedial component is tailored to respond to one or another of those vestiges, we can only conclude that the sweeping remedy imposed here exceeded the admittedly broad power of the district court.
C. Capacity and Standing
The State argues that because of the doctrine of municipal incapacity, its political subdivisions — the Yonkers parties— cannot press their cross-claim against the State. See generally Kelley v. Metropolitan County Bd. of Educ., 836 F.2d 986, 988 (6th Cir.1987). In a related argument, the State contends that the NAACP lacks standing to litigate how remedial funding is allocated between the State and the local defendants. See generally DeKalb County School Dist. v. Schrenko, 109 F.3d 680, 688-89, 693 (11th Cir.1997). These are questions of law that we review de novo. *319See Fund for Animals v. Babbitt, 89 F.3d 128, 132 (2d Cir.1996). We must briefly address the State’s municipal incapacity and standing arguments because they are necessary predicates to the State’s challenge to the allocation of funding responsibility for EIP I between the State and City.
Although we reject the State’s arguments now, we reach no conclusion as to whether they may take on force in any further stage of the litigation, such as claims in the nature of contribution after unitary status has been achieved and declared.
1. Waiver
The Board argues that the State has waived its municipal incapacity defense, and relies on Fed.R.Civ.P. 9(a), which requires parties raising a defense involving “the capacity of any party to sue” to do so by pleading in a “specific negative averment.” We will assume without deciding that a party waives a capacity defense if the party fails to raise it within the contemplation of Rule 9. See 5 Charles Alan Wright & Arthur R. Miller, Federal Practice and Procedure § 1295, at 574-75 (2d ed.1990). Likewise, we will assume without deciding that the State’s municipal incapacity defense comes within the scope of Rule 9.
The State did not specifically raise its incapacity defense in its answer to the Board of Education’s cross-claim. It did, however, include such an averment in its answer to the City’s later cross-claim. Therefore, even if the Board’s waiver argument is correct, we would still have to reach the merits of the incapacity claim. In a case in which the funding questions are all interrelated, it would make little sense for us to evaluate this defense as against the City but not as against the Board. We will therefore go to the merits.
2. Merits of the Defenses
We start with the State’s concession in this case that the NAACP has standing to “litigate the State’s liability and the scope of the remedy.” Br. of Appellant State of New York at 81. It follows that even if the State prevailed on its claims as to Yonkers’ incapacity and the NAACP’s lack of standing on apportionment, (1) the State would remain a properly joined defendant; (2) the State would remain an adjudicated constitutional tort-feasor in a case as to which (3) no declaration of unitary status has found that the constitutional injuries flowing from segregation has been fully redressed; and (4) the State would remain subject to the remedial authority of the district court. The State has failed to explain how, in light of its concession, the district court could avoid apportioning liability in some way between the State and the local defendants. See Alberti v. Sheriff of Harris County, 937 F.2d 984, 1001 n. 8 (5th Cir.1991). It would make little sense for the district court to have this authority to allocate responsibility, yet bar the parties from having a say about it.
A number of institutional reform cases have implemented apportionment of liability between states and their subdivisions. See, e.g., Milliken v. Bradley, 433 U.S. at 291, 97 S.Ct. at 2762-63 (finding no violation of “principles of federalism” when district court ordered state defendants to bear half the costs of desegregation remedies); Benjamin v. Malcolm, 803 F.2d 46, 54 (2d Cir.1986) (finding City of New York possessed standing to bring cross-claim for injunctive relief against State when State’s refusal to accept transfer of sufficient number of prisoners had led to unconstitutional conditions in City prisons). True, these cases do not address the precise incapacity and standing issues now raised by the State. But having raised these issues, the State has failed to articulate how the district court should proceed were the State to prevail on them, or why the NAACP should not be heard on the apportionment issue (in light of the State’s concession), or what difference it makes if Yonkers is heard as well.
*320Our rejection of the State’s arguments concerning incapacity and standing is limited to the case as it is currently structured, in which there is an equitable action with joint tortfeasors, ongoing prospective relief, and no finding that the constitutional injuries have been redressed. It is this last factor that distinguishes this case from Schrenko, on which the State relies in advancing its standing argument. In that case, the school district at issue had been deemed unitary, meaning that all injuries had been remedied. See Schrenko, 109 F.3d at 692. With the case in that posture, the individual plaintiffs of course lacked standing to litigate what was essentially a contribution claim between defendants. See id. at 689.
D. Apportionment of Costs
Having rejected the State’s municipal incapacity and standing arguments for the time being, we proceed to the merits of its objections to the district court’s funding orders. The State’s principal objection is to the requirement that it be required to share equally in the annual costs of EIP I. The State contends that the district court should apportion liability by degree of fault, a method that would reduce the State’s share significantly.
The district court has broad equitable discretion to apportion remedial costs among joint tortfeasors. See Milliken, 433 U.S. at 288-91, 97 S.Ct. at 2761-63 (affirming district court’s conclusion that half the remedial costs for desegregation of Detroit schools be paid by the state of Michigan). In apportioning costs, courts will assess both ability to pay and relative degrees of fault, but the overriding concern is that the remedy be fully funded. See Green v. County School Bd., 391 U.S. 430, 439, 88 S.Ct. 1689, 1694, 20 L.Ed.2d 716 (1968) (desegregation remedy must “promise[] realistically to work, and ... realistically to work now”). The district court found that the City and State were equally responsible for segregation in Yonkers, and that the sharing formula assessed a “fair and proportionate” burden on the levels of government, given their ability to pay.
We cannot say that the court’s factual findings about degree of fault are clearly erroneous or that it abused its broad remedial discretion in apportioning compliance costs in this manner.
A related issue is the State’s argument that any required State contribution to EIP I should be offset by the State’s substantial annual magnet school aid, which has a remedial tendency and purpose (and which New York provides to other large school districts). The district court rejected this argument, a decision the State argues is unfair, and an unwarranted intrusion into state sovereignty. We conclude that it was not an abuse of the court’s broad discretion to deny the State credit for payments it has already made to Yonkers through magnet school grants. In making its decision, the Court did not recharacterize the subjective intent of the legislature, as the State argues, but instead determined that this money did not have the effect of funding the ordered remedy. We do not find that conclusion to be clearly erroneous.4
CONCLUSION
For the foregoing reasons, we reverse the district court’s vestiges finding and its remedial order. . We affirm its order imposing an equal apportionment of costs between the State and Yonkers for funding the previous remedy. We remand the case for further proceedings consistent with Freeman v. Pitts, 503 U.S. 467, 112 S.Ct. 1430, 118 L.Ed.2d 108 (1992), Board of Education v. Dowell, 498 U.S. 237, 111 *321S.Ct. 630, 112 L.Ed.2d 716 (1991), and this opinion.
. The district court used two standards for determining whether a school was desegregated. For a magnet school, the minority enrollment had to be within 15 percentage points of the system-wide minority population in the first year and within 10 points in all subsequent years. For non-magnet schools, the figure was 20 percentage points. See Yonkers III, 837 F.2d at 1215.
. The Board proffered testimony that, in some classrooms, students of the same race sat in clusters — something that could be attributed to cliques and affinities among students. The Board has floated the idea that these groupings may have been segregative seating assignment by teachers, but counsel for the Board was unable to say at oral argument why, if such an outrageous practice existed, it could not be rectified by Board-imposed discipline or dismissal, without remedial funding from the State.
. In partial dissent, Judge Sack would return this case to the district court for a clearer articulation of its factual findings. We conclude, however, that the defect of the district court opinion — the absence of affirmable findings concerning vestiges of discrimination— would not be remedied by remand.
The district judge is steeped in the law of this case, and has a commanding knowledge of its facts. There are talented lawyers on all sides. There is no reason to assume that the absence of affirmable facts in the district court opinion is attributable to any oversight by the district judge (or by the lawyers) or any failure to take pains or to appreciate what is required. And we have conducted our own careful scrutiny of the record, to see if it could support findings of vestige and to justify a remand if anything were there. Our review has been guided by counsel having a great incentive and a full opportunity to highlight any evidence pointing to the existence of vestiges. In the end, we are convinced that a remand would waste judicial resources and put off what in the end would be the same result.
Absent good reason to remand, we will decide the appeal on the record before us. See, e.g., Chase Manhattan Bank, N.A. v. American Nat’l Bank & Trust Co., 93 F.3d 1064, 1072 (2d Cir.1996); Stetson v. Howard D. Wolf & Assocs., 955 F.2d 847, 850 (2d Cir.1992) (“An appellate court has the power to decide cases on appeal if the facts in the record adequately support the proper result.”); English v. Town of Huntington, 448 F.2d 319, 321 (2d Cir.1971) (“[W]e can discern enough solid facts from the record to enable us to render a decision.”); Leighton v. One William St. Fund, Inc., 343 F.2d 565, 567 (2d Cir.1965); Rossiter v. Vogel, 148 F.2d 292, 293 (2d Cir.1945) ("[F]indings ‘are not a jurisdictional requirement of appeal,’ but only ‘aid appellate courts in reviewing the decision below.' " (quoting Hurwitz v. Hurwitz, 136 F.2d 796, 799 (D.C.Cir.1943))); 9A Charles Alan Wright & Arthur R. Miller, Federal Practice and Procedure § 2577, at 522-23 (2d ed. 1995) (“[I]t is settled that compliance with Rule 52 is not jurisdictional and the appellate court may decide the appeal without further findings if it feels that it is in a position to do so.”).
. The State wishes to preserve its argument that it cannot be held liable as a matter of law for the acts and omissions the district court and this Court have found contributed to seg-regalion in Yonkers, so it raises the argument here again. We reject it for the same reasons we adduced in 1996. See Yonkers V, 96 F.3d 600 (2d Cir.1996).