opinion: Mr. Justice Rehnquist
  delivered the opinion of the Court.
  This school desegregation action comes to us after five years and two round trips through the lower federal courts. Those protracted proceedings have been devoted to the formulation of a remedy for actions of the Dayton Board of Education found to be in violation of the Equal Protection Clause of the Fourteenth Amendment. In the decision now under review, the Court of Appeals for the Sixth Circuit finally approved a plan involving districtwide racial-distribution requirements, after rejecting two previous, less sweeping orders by the District Court. The plan required, beginning with the 1976-1977 school year, that the racial distribution of each school in the district be brought within 15% of the 48%-52% black-white population ratio of Dayton. As finally formulated, the plan employed a variety of desegregation techniques, including the “pairing” of schools, the redefinition of attendance zones, and a variety of centralized special programs and “magnet schools.” We granted certiorari, 429 U. S. 1060 (1977), to consider the propriety of this court-ordered remedy in light of the constitutional violations which were found by the courts below.
  Whatever public notice this case has received as it wended its way from the United States District Court for the Southern District of Ohio to this Court has been due to the fact that it represented an effort by minority plaintiffs to obtain relief from alleged unconstitutional segregation of the Dayton public schools said to have resulted from actions by the petitioner School Board. While we would by no means discount the importance of this aspect of the case, we think that the case is every bit as important for the issues it raises as to the proper allocation of functions between the district courts and the courts of appeals within the federal judicial system.
  Indeed, the importance of the judicial administration aspects of the case are heightened by the presence of the substantive issues on which it turns. The proper observance of the division of functions between the federal trial courts and the federal appellate courts is important in every case. It is especially important in a case such as this where the District Court for the Southern District of Ohio was not simply asked to render judgment in accordance with the law of Ohio in favor of one private party against another; it was asked by the plaintiffs, parents of students in the public school system of a large city, to restructure the administration of that system.
  There is no doubt that federal courts have authority to grant appropriate relief of this sort when constitutional violations on the part of school officials are proved. Keyes v. School District No. 1, Denver, Colo., 413 U. S. 189 (1973); Wright v. Council of City of Emporia, 407 U. S. 451 (1972); Swann v. Charlotte-Mecklenburg Board of Education, 402 U. S. 1 (1971). But our cases have just as firmly recognized that local autonomy of school districts is a vital national tradition. Milliken v. Bradley, 418 U. S. 717, 741-742 (1974); San Antonio School District v. Rodriguez, 411 U. S. 1, 50 (1973); Wright v. Council of City of Emporia, supra, at 469. It is for this reason that the case for displacement of the local authorities by a federal court in a school desegregation case must be satisfactorily established by factual proof and justified by a reasoned statement of legal principles. Cf. Pasadena City Board of Education v. Spangler, 427 U. S. 424 (1976).
  The lawsuit was begun in April 1972, and the District Court filed its original decision on February 7, 1973. The District Court first surveyed the past conduct of affairs by the Dayton School Board, and found “isolated but repeated instances of failure by the Dayton School Board to meet the standards of the Ohio law mandating an integrated school system.” It cited instances of physical segregation in the schools during the early decades of this century, but concluded that “[b]oth by reason of the substantial time that [had] elapsed and because these practices have ceased, . . . the foregoing will not necessarily be deemed to be evidence of a continuing segrega-tive policy.”
  The District Court also found that as recently as the 1950’s, faculty hiring had not been on a racially neutral basis, but that “[b]y 1963, under a policy designated as one of 'dynamic gradualism,’ at least one black teacher had been assigned to all eleven high schools and to 35 of the 66 schools in the entire system.” It further found that by 1969 each school in the Dayton system had an integrated teaching staff consisting of at least one black faculty member. The court’s conclusion with respect to faculty hiring was that pursuant to a 1971 agreement with the Department of Health, Education, and Welfare, “the teaching staff of the Dayton public schools became and still remains substantially intégrated.”
  The District Court noted that Dunbar High School had been established in 1933 as a black high school, taught by black teachers and attended by black pupils. At the time of its creation there were no attendance zones in Dayton and students were permitted liberal transfers, so that attendance at Dunbar was voluntary. The court found that Dunbar continued to exist as a citywide all-black high school until it closed in 1962.
  Turning to more recent operations of the Dayton public schools, the District Court found that the “great majority” of the 66 schools were imbalanced and that, with one exception, the Dayton School Board had made no affirmative effort to achieve racial balance within those schools. But the court stated that there was no evidence of racial discrimination in the establishment or alteration of attendance boundaries or in the site selection and construction of new schools and school additions. It considered the use of optional attendance zones within the district, and concluded that in the majority of cases the “optional zones had no racial significance at the time of their creation.” It made a somewhat ambiguous finding as to the effect of some of the zones in the past, and concluded that although none of the optional elementary school attendance zones today “have any significant potential effects in terms of increased racial separation,” the same cannot be said of the optional high school zones. Two zones in particular, “those between Roosevelt and Colonel White and between Kiser and Colonel White, are by far the largest in the system and have had the most demonstrable racial effects in the past.”
  The court found no evidence that the district’s “freedom of enrollment” policy had “been unfairly operated or that black students [had] been denied transfers because of their race.” Finally the court considered action by a newly elected Board on January 3, 1972, rescinding resolutions, passed by the previous Board, which had acknowledged a role played by the Board in the creation of segregative racial patterns and had called for various types of remedial measures. The District Court’s ultimate conclusion was that the “racially imbalanced schools, optional attendance zones, and recent Board action ... are cumulatively in violation of the Equal Protection Clause.”
  The District Court’s use of the phrase “cumulative violation” is unfortunately not free from ambiguity. Treated most favorably to the respondents, it may be said to represent the District Court’s opinion that there were three separate although relatively isolated instances of unconstitutional action on the part of petitioners. Treated most favorably to the petitioners, however, they must be viewed in quite a different light. The finding that the pupil population in the various Dayton schools is not homogeneous, standing by itself, is not a violation of the Fourteenth Amendment in the absence of a showing that this condition resulted from intentionally segregative actions on the part of the Board. Washington v. Davis, 426 U. S. 229, 239 (1976). The District Court’s finding as to the effect of the optional attendance zones for the three Dayton high schools, assuming that it was a violation under the standards of Washington v. Davis, supra, appears to be so only with respect to high school districting. Swann, 402 U. S., at 15. The District Court’s conclusion that the Board’s rescission of previously adopted School Board resolutions was itself a constitutional violation is also of questionable validity.
  The Board had not acted to undo operative regulations affecting the assignment of pupils or other aspects of the management of school affairs, cf. Reitman v. Mulkey, 387 U. S. 369 (1967), but simply repudiated a resolution of a predecessor Board stating that it recognized its own fault in not taking affirmative action at an earlier date. We agree with the Court of Appeals’ treatment of this action, wherein that court said:
  “The question of whether a rescission of previous Board action is in and of itself a violation of appellants’ constitutional rights is inextricably bound up with the question of whether the Board was under a constitutional duty to take the action which it initially took. Cf. Hunter v. Erickson, 393 U. S. 385 . . . (1969); Gomillion v. Lightfoot, 364 U. S. 339 . . . (1960). If the Board was not under such a duty, then the rescission of the initial action in and of itself cannot be a constitutional violation. If the Board was under such a duty, then the rescission becomes a part of the cumulative violation, and it is not necessary to ascertain whether the rescission ipso facto is an independent violation of the Constitution.” Brinkman v. Gilligan, 503 F. 2d 684, 697 (1974).
  Judged most favorably to the petitioners, then, the District Court’s findings of constitutional violations did not, under our cases, suffice to justify the remedy imposed. Nor is light cast upon the District Court’s finding by its repeated use of the phrase “cumulative violation.” We realize, of course, that the task of factfinding in a case such as this is a good deal more difficult than is typically the case in a more orthodox lawsuit. Findings as to the motivations of multimembered public bodies are of necessity difficult, cf. Arlington Heights v. Metropolitan Housing Dev. Corp., 429 U. S. 252 (1977), and the question of whether demographic changes resulting in racial concentration occurred from purely neutral public actions or were instead the intended result of actions which appeared neutral on their face but were in fact invidiously discriminatory is not an easy one to resolve.
  We think it accurate to say that the District Court’s formulation of a remedy on the basis of the three-part “cumulative violation” was certainly not based on an unduly cautious understanding of its authority in such a situation. The remedy which it originally propounded in light of these findings of fact included requirements that optional attendance zones be eliminated, and that faculty assignment practices and hiring policies with respect to classified personnel be tailored to achieve representative racial distribution in all schools. The one portion of the remedial plan submitted by the School Board which the District Court refused to accept without change was that which dealt with so-called “freedom of enrollment priorities.” The court ordered that, as applied to high schools, new students at each school be chosen at random from those wishing to attend. The Board was required to furnish transportation for all students who chose to attend a high school outside the attendance area of their residence.
  Both the plaintiffs and the defendant School Board appealed the order of the District Court to the United States Court of Appeals for the Sixth Circuit. Brinkman v. Gilligan, supra. That court considered at somewhat greater length than had the District Court both the historical instances of alleged racial discrimination by the Dayton School Board and the circumstances surrounding the adoption of the Board’s resolutions and the subsequent rescission of those resolutions. This consideration was in a purely descriptive vein: no findings of fact made by the District Court were reversed as having been clearly erroneous, and the Court of Appeals engaged in no factfinding of its own based on evidence adduced before the District Court. The Court of Appeals then focused on the District Court’s finding of a three-part “cumulative” constitutional violation consisting of racially imbalanced schools, optional attendance zones, and the rescission of the Board resolutions. It found these to be “amply supported by the evidence.”
  Plaintiffs in the District Court, respondents here, had cross-appealed from the order of the District Court, contending that the District Court had erred in failing to make further findings tending to show segregative actions on the part of the Dayton School Board, but the Court of Appeals found it unnecessary to pass on these contentions. The Court of Appeals also stated that it was unnecessary to “pass on the question of whether the rescission [of the Board resolutions] by itself was a violation of” constitutional rights. It did discuss at length what it described as “serious questions” as to whether Board conduct relating to staff assignment, school construction, grade structure and reorganization, and transfers and transportation, should have been included within the “cumulative violation” found by the District Court. But it did no more than discuss these questions; it neither upset the factual findings of the District Court nor reversed the District Court’s conclusions of law.
  Thus, the Court of Appeals, over and above its historical discussion of the Dayton school situation, dealt with and upheld only the three-part “cumulative violation” found by the District Court. But it nonetheless reversed the District Court’s approval of the School Board plan as modified by the District Court, because the Court of Appeals concluded that “the remedy ordered ... is inadequate, considering the scope of the cumulative violations.” While it did not discuss the specifics of any plan to be adopted on remand, it repeated the admonition that the court’s duty is to eliminate “all vestiges of state-imposed school segregation.” Keyes, 413 U. S., at 202; Swann, 402 U. S., at 15.
  Viewing the findings of the District Court as to the three-part “cumulative violation” in the strongest light for the respondents, the Court of Appeals simply had no warrant in our cases for imposing the systemwide remedy which it apparently did. There had been no showing that such a remedy was necessary to “eliminate all vestiges of the state-imposed school segregation.” It is clear from the findings of the District Court that Dayton is a racially mixed community, and that many of its schools are either predominantly white or predominantly black. This fact without more, of course, does not offend the Constitution. Spencer v. Kugler, 404 U. S. 1027 (1972); Swann, supra, at 24. The Court of Appeals seems to have viewed the present structure of the Dayton school system as a sort of “fruit of the poisonous tree,” since some of the racial imbalance that presently obtains may have resulted in some part from the three instances of seg-regative action found by the District Court. But instead of tailoring a remedy commensurate to the three specific violations, the Court of Appeals imposed a systemwide remedy going beyond their scope.
  On appeal, the task of a court of appeals is defined with relative clarity; it is confined by law and precedent, just as are those of the district courts and of this Court. If it concludes that the findings of the district court are clearly erroneous, it may set them aside under Fed. Rule Civ. Proc. 52 (a). If it decides that the district court has misapprehended the law, it may accept that court’s findings of fact but reverse its judgment because of legal errors. Here, however, as we conceive the situation, the Court of Appeals did neither. It was vaguely dissatisfied with the limited character of the remedy which the District Court had afforded plaintiffs, and proceeded to institute a far more sweeping one of its own, without in any way upsetting the District Court’s findings of fact or reversing its conclusions of law.
  The Court of Appeals did not actually specify a remedy, but did, in increasingly strong language in subsequent opinions, require that any plan eliminate systemwide patterns of one-race schools predominant in the district. Brinkman v. Gilligan, 518 F. 2d 853, 855 (1975). In the face of this commandment, the District Court, after twice being reversed, observed:
  “This court now reaches the reluctant conclusion that there exists no feasible method of complying with the mandate of the United States Court of Appeals for the Sixth Circuit without the transportation of a substantial number of students in the Dayton school system. Based upon the plans of both the plaintiff and defendant the assumption must be that the transportation of approximately 15,000 students on a regular and permanent basis will be required.”
  We think that the District Court would have been insensitive indeed to the nuances of the repeated reversals of its orders by the Court of Appeals had it not reached this conclusion. In effect, the Court of Appeals imposed a remedy which we think is entirely out of proportion to the constitutional violations found by the District Court, taking those findings of violations in the light most favorable to respondents.
  This is not to say that the last word has been spoken as to the correctness of the District Court’s findings as to unconstitutionally segregative actions on the part of the petitioners. As we have noted, respondents appealed from the initial decision and order of the District Court, asserting that additional violations should have been found by that court. The Court of Appeals found it unnecessary to pass upon the respondents’ contentions in its first decision, and respondents have not cross-petitioned for certiorari in this Court from the decision of the Court of Appeals. Nonetheless, they are entitled under our precedents to urge any grounds which would lend support to the judgment below, and we think that their contentions of unconstitutionally segregative actions, in addition to those found as fact by the District Court, fall into this category. In view of the confusion at various stages in this case, evident from the opinions both of the Court of Appeals and the District Court, as to the applicable principles and appropriate relief, the case must be remanded to the District Court for the making of more specific findings and, if necessary, the taking of additional evidence.
  If the only deficiency in the record before us were the failure of the Court of Appeals to pass on respondents’ assignments of error respecting the initial rulings of the District Court, it would be appropriate to remand the case. But we think it evident that supplementation of the record will be necessary. Apart from what has been said above with respect to the use of the ambiguous phrase “cumulative violation” by both courts, the disparity between the evidence of constitutional violations and the sweeping remedy finally decreed requires supplementation of the record and additional findings addressed specifically to the scope of the remedy. It is clear that the presently mandated remedy cannot stand upon the basis of the violations found by the District Court.
  The District Court, in the first instance, subject to review by the Court of Appeals, must make new findings and conclusions as to violations in the light of this opinion, Washington v. Davis, 426 U. S. 229 (1976), and Arlington Heights v. Metropolitan Housing Dev. Corp., 429 U. S. 252 (1977). It must then fashion a remedy in the light of the rule laid down in Swann, and elaborated upon in Hills v. Gautreaux, 425 U. S. 284 (1976). The power of the federal courts to restructure the operation of local and state governmental entities “is not plenary. It ‘may be exercised “only on the basis of a constitutional violation.” ’ [Milliken v. Bradley], 418 U. S., at 738, quoting Swann v. Charlotte-Mecklenburg Board of Education, 402 U. S. 1, 16. See Rizzo v. Goode, 423 U. S. 362, 377. Once a constitutional violation is found, a federal court is required to tailor ‘the scope of the remedy’ to fit ‘the nature and extent of the constitutional violation.’ 418 U. S., at 744; Swann, supra, at 16.” Id., at 293-294. See also Austin Independent School Dist. v. United States, 429 U. S. 990, 991 (1976) (Powell, J., concurring).
  The duty of both the District Court and the Court of Appeals in a case such as this, where mandatory segregation by law of the races in the schools has long since' ceased, is to first determine whether there was any action in the conduct of the business of the School Board which are intended to, and did in fact, discriminate against minority pupils, teachers, or staff. Washington v. Davis, supra. All parties should be free to introduce such additional testimony and other evidence as the District Court may deem appropriate. If such violations are found, the District Court in the first instance, subject to review by the Court of Appeals, must determine how much incremental segregative effect these violations had on the racial distribution of the Dayton school population as presently constituted, when that distribution is compared to what it would have been in the absence of such constitutional violations. The remedy must be designed to redress that difference, and only if there has been a systemwide impact may there be a systemwide remedy. Keyes, 413 U. S., at 213.
  We realize that this is a difficult task, and that it is much easier for a reviewing court to fault ambiguous phrases such as “cumulative violation” than it is for the finder of fact to make the complex factual determinations in the first instance. Nonetheless, that is what the Constitution and our cases call for, and that is what must be done in this case.
  While we have found that the plan implicitly, if not explicitly, imposed by the Court of Appeals was erroneous on the present state of the record, it is undisputed that it has been in effect in the Dayton school system during the present year without creating serious problems. While a school board and a school constituency which attempt to comply with a plan to the best of their ability should not be penalized, we think that the plan finally adopted by the District Court should remain in effect for the coming school year subject to such further orders of the District Court as it may find warranted following the hearings mandated by this opinion.
  The judgment of the Court of Appeals is vacated, and the cause is remanded for further proceedings consistent with this opinion.
  It is so ordered.
  Mr. Justice Marshall took no part in the consideration or decision of this case.
  This action was filed on April 17, 1972, by parents of black children attending schools operated by the defendant Dayton Board of Education. After an expedited hearing between November 13 and December 1, 1972, the District Court for the Southern District of Ohio, on February 7, 1973, rendered findings of fact and conclusions of law directing the formulation of a desegregation plan. App. 1. On July 13, 1973, that court approved, with certain modifications, a plan proposed by the School Board. On appeal to the Court of Appeals for the Sixth Circuit, that court affirmed the findings of fact but reversed and remanded as to the proposed remedial plan. Brinkman v. Gilligan, 503 F. 2d 684 (CA6 1974).
  The District Court then ordered the submission of new plans by the Board and by any other interested parties. App. 70. On March 10, 1975, it rejected a plan proposed by the plaintiffs, and, with some modifications, approved the Board's plan as modified and expanded in an effort to comply with the Court of Appeals mandate. Id., at 73. On appeal, the Court of Appeals again reversed as to remedy and directed that the District Court “adopt a system-wide plan for the 1976-1977 school year . . . .” Brinkman v. Gilligan, 518 F. 2d 853 (1975).
  Upon this second remand, the District Court, on December 29, 1975, ordered formulation of the plan whose terms are developed below. App. 99. On March 25, 1976, the details of the plan were approved by the District Court. Id., at 114. In the decision now under review, the Court of Appeals affirmed. Brinkman v. Gilligan, 539 F. 2d 1084 (1976).
  The District Court said that it would deal on a case-by-case basis with failures to bring individual schools into compliance with this requirement. It also ordered that students already enrolled in the 10th and 11th grades be allowed to finish in their present high schools, and announced the following “guidelines” to be followed “whenever possible” in the case of elementary school students:
  “1. Students may attend neighborhood walk-in schools in those neighborhoods where the schools already have the approved ratio ;
  “2. Students should be transported to the nearest available school;
  “3. No student should be transported for a period of time exceeding twenty (20) minutes, or two (2) miles, whichever is shorter.” App. 104.
  “Pairing” is the designation of two Or more schools with contrasting racial composition for an exchange program where a large proportion of the students in each school attend the paired school for some period. In the plan adopted, by the District Court, it was the primary remedy used in the ease of elementary schools.
  The court pointed out that since 1888 Ohio law as construed by the Ohio Supreme Court has forbidden separate public schools for black and white children. See Ohio Rev. Code Ann. §3313.48 (1972); Board of Education v. State, 45 Ohio St. 555, 16 N. E. 373 (1888).
  “Such instances include a physical segregation into separate buddings of pupils and teachers by race at the Garfield School in the early 1920’s, a denial to blacks of access to swimming pools in high schools in the 1930’s and 1940’s and the exclusion, between 1938 and 1948, of black high school teams from the city athletic conference.” App. 2-3 (footnote omitted).
  The court also considered employment of nonteaching personnel, and observed that blacks made up a proportion of the nonteaching, nonadministrative personnel equal to the proportion of black students in the district, though in certain occupations they were represented at a substantially lower rate.
  The court noted that a concerted effort had been made in the past few years to enroll more black students at the Patterson Co-op High School.
  An optional zone is an area between two attendance zones, the student residents of which are free to choose which of the two schools they wish to attend.
  The District Court found that three optional high school zones “may have” had racial significance at the time of their creation.
  The following information about those zones is contained in an appendix to the District Court opinion:
  % black population High Schools Date of creation At date of creation 1972-73
  Roosevelt/ . 1951 31.5 100.0
  Colonel White (extended 1958) 0.0 54.6
  Kiser/ . 1962 2.7 9.8
  Colonel White 1-1 54.6
  The District Court’s first plan also contained the following provisions:
  (V) Establishment of four citywide elementary science centers the enrollment of which would approximate the existing black-white ratio of students in the system;
  (VI) Combination of two high schools into a unified cooperative school with districtwide attendance areas;
  (VII) Formation of elementary and high, school all-city bands, orchestras, and choruses;
  (VIII) Provisions for scheduling of integrated athletics;
  (IX) Establishment of a minority language program for education of staff;
  (X) Utilization of the Living Arts Center for inter-racial experiences in art, creative writing, dance, and drama;
  (XI) Creation of centers for rumor control, school guidance, and area learning. See App. 35-36.
  The court thus eliminated a provision within the Board plan which gave first priority to students residing within the school’s attendance zone.