This school desegregation case was originally filed almost thirteen years ago in October, 1970.1 The long factual and procedural history of this litigation is set forth in our earlier opinions, Tasby v. Estes (Tasby II), 572 F.2d 1010 (5th Cir.1978), cert. dismissed, 444 U.S. 437, 100 S.Ct. 716, 62 L.Ed.2d 626 (1980); Tasby v. Estes (Tasby I), 517 F.2d 92 (5th Cir.), cert. denied, 423 U.S. 939, 96 S.Ct. 299, 46 L.Ed.2d 271 (1975), and we see no need to repeat that history here. We note only that the case has come a long way in the intervening years and that it has now reached the point where the major portion of the district court’s judgment is the result of the parties’ own agreement.
I. PROCEEDINGS IN THE DISTRICT COURT.
In Tasby II, we were concerned with the substantial number of one-race schools2 left in existence under the desegregation plan approved by the district court, and with the absence of specific findings as to the feasibility of using the techniques approved by the Supreme Court in Swann v. Gharlotte-Meckienburg Board of Education, 402 U.S. 1, 91 S.Ct. 1267, 28 L.Ed.2d 554 (1971), to desegregate further the Dallas Independent School District (“DISD”). 572 F.2d at 1014. We remanded the case to the district court for
the formulation of a new student assignment plan and for findings to justify the maintenance of any one-race schools that may be a part of that plan. The district court is directed to include in its plan a majority-to-minority transfer option with adequate transportation. As for the remaining provisions of its order here under review, the district court is to reassess such provisions in light of the remedy it fashions with respect to school assignments.
Id. at 1018.
On remand, the district court held an extensive hearing and rendered a sensitive, thorough opinion in an attempt to address our concerns. Tasby v. Estes, 520 F.Supp. 683 (N.D.Tex.1981). The court concluded that the mandatory transportation technique suggested in Swann was not feasible within the DISD because of substantial time and distance problems, as well as a shortage of enough anglo students to go around.3 520 F.Supp. at 733, 735, 739. It directed the parties to develop a plan that would obtain greater desegregation within the school system and would attempt to eliminate the achievement gap between anglo and minority students.
*92The parties entered into a stipulation addressing four areas of judicial concern.4 The DISD agreed: 1) to implement modifications to the majority-to-minority transfer program and to consider suggestions in formulating a majority-to-minority publicity program; 2) to consider and develop programmatic remedies to “reduce and hopefully to eliminate the achievement disparity between minority and anglo students,” and to allocate fifty dollars annually per “ethnic minority student ... in predominately ethnic minority (more than 75%) schools” to be used for these programmatic remedies; 3) to improve the facilities at the Nolan Estes Educational Plaza; and 4) to expand and improve the magnet school program. 10 Record at 1967. The district court approved this stipulation and included it in the court’s final judgment.
The parties were unable to agree on a plan with respect to two items of concern mentioned by the district court, and their continuing disagreement forms the basis for this appeal. First, the court had asked the parties to address the feasibility of obtaining greater desegregation by adjusting contiguous attendance zones. In particular, the court was concerned about the continuing existence of predominately anglo schools.5 The plaintiffs suggested alterations in the attendance zones of naturally desegregated schools, while the DISD and the Curry and Brinegar intervenors rejected any such alterations. They suggested, instead, reliance on the majority-to-minority transfer and magnet school programs. The district court approved the plaintiffs’ proposal with a minor variation not relevant here.
The second area of disagreement involves the Minority Neighborhood Option Plan (“MNOP”), which was proposed by the Black Coalition. The Coalition, a new party to this litigation, is a group of minority parents who desired the option of having their children remain in neighborhood 4-8 centers; in essence, they sought to opt out of the mandatory busing ordered by the district court in 1976. The plaintiffs, the NAACP and the Cunningham intervenors opposed adoption of this plan because they believed that it would resegregate a significant portion of the 4-8 schools. The Coalition, the DISD, and the Curry and Brinegar intervenors insisted that minority members have the right to opt out of a desegregated system. The district court refused to accept the MNOP plan because it could not reconcile such a plan with traditional legal principles favoring maximum desegregation or with this court’s concern about the continued existence of one-race schools.
The DISD, and the Curry and Brinegar intervenors have appealed from the district court’s decision. All three challenge the district court’s: 1) failure to find that the DISD has converted to a unitary school system; 2) rejection of the MNOP plan; and 3) alteration of the attendance zones for Woodrow Wilson and Thomas Jefferson High Schools, in an attempt to desegregate further Bryan Adams and W.T. White High Schools. The Curry intervenors have also appealed the court’s revision of the DISD minority hiring and promotion goals.
Before we proceed to address these contentions, we believe it worthwhile to note what has not been appealed. First of all, the parties who have been urging increased desegregation — the original plaintiffs, the NAACP and the Cunningham intervenors— appear to be satisfied with the district court’s decision. The NAACP initially filed an appeal but subsequently withdrew it because the organization determined that the court’s decision, if not an optimum solution, was constitutionally permissible. Thus, no one has challenged on appeal the court’s conclusion that systemwide mandatory transportation is not feasible or the adequacy of the court’s order as a remedy for past constitutional violations. On the other side of the litigation, the Black Coalition has not *93appealed the court’s rejection of its MNOP plan; this court is urged to require approval of the plan solely by the DISD and the Curry and Brinegar intervenors. Similarly, the Curry intervenors are the only parties to challenge the personnel revisions; the DISD has informed this court that it can “live with” the district court’s changes. Finally, the appellants’ objections to the court’s alteration of attendance zones in North and East Dallas concern less than one-percent of the DISD students.
In light of the present impressive level of agreement in this case, we can only say that the district court has done a commendable job with what was once a massive undertaking. With the exception of the alteration of the East Dallas attendance zones, the district court’s decision is affirmed.
II. UNITARY STATUS.
When this case was last before us in 1978, the DISD had acknowledged that the “creation of the all black East Oak Cliff subdistrict and the existence of a substantial number of one-race schools militate[d] against the finding of a unitary school system.” Tasby II, 572 F.2d at 1014. The DISD has now decided that it is time for judicial supervision of the Dallas school system to end; therefore, it maintains that the district court should have declared the school system to be unitary.6 On the record before us, we cannot say that the district court erred in failing to make such a declaration for the purposes of this proceeding.
The appellants insist that the DISD is like the school systems in Houston and Atlanta, both of which have been declared unitary. Ross v. Houston Independent School District, 699 F.2d 218 (5th Cir.1983); Calhoun v. Cook, 522 F.2d 717 (5th Cir. 1975). Of course, the fact that we held that the district courts’ determinations of unitary status were not clearly erroneous, see Ross, supra, 699 F.2d at 226, in those cases does not necessarily indicate that the converse is true in this case. We must “keep in mind that each school district is unique,” Ross, 699 F.2d at 227, and we note that there are important differences among the three cases. For example, the plaintiffs in Ross had not come up with any proposal that would have further desegregated the Houston school system. The same cannot be said in this case. The Ross court was presented with
the undisputed fact that HISD is unitary in every aspect but the existence of a homogeneous student population; the intensive efforts that have been made to eliminate one-race schools; and the district court’s conclusion that further measures would be both impractical and detrimental to education ....
699 F.2d at 228. Here, there remains some dispute about the DISD’s overall unitary character. Further, while the court found that the DISD had made a good faith effort to comply with the court’s orders, it also noted that the DISD had opposed any student reassignments for purposes of desegregation “no matter how feasible or how minimal.” 10 Record at 2020. The court added that “[s]o far as [it could] ascertain, the District has never voluntarily moved to desegregate the Dallas school system; every step toward desegregation has been due to court action.” Id. Moreover, in the present case, unlike Ross, the relevant proceeding before the district court was held pursuant to, and for the purpose of complying with the directions of, a mandate of this court to hold hearings to formulate certain desegregation remedies. In Ross, the proceeding held to comply with this court’s last mandate had taken place long previously.
The Curry intervenors argue that the district court improperly shifted the burden of proving that the remaining one-race schools were not vestiges of past segregation onto the school officials, and that its reliance on Keyes v. School District No. 1, 413 U.S. 189, 208, 93 S.Ct. 2686, 2697, 37 L.Ed.2d 548 (1973) (prima facie case of “unlawful segregative design on the part of school authorities ... shifts to those authorities the bur*94den of proving that other segregated schools within the system are not also the result of intentionally segregative actions”) was misplaced. The intervenors insist that the plaintiffs bore the burden of proving “that a causal nexus exists between current segregated conditions in a school district and former segregative intent (de jure segregation) on the part of the state.” Curry Brief at 7.
While the district court may have relied on the wrong case for its presumption, the court was absolutely correct in placing on the school authorities the burden of proving that the remaining one-race schools were not vestiges of the past unlawful segregation. The Reyes presumption cited by the district court involves proof of de jure discrimination in a school system where school segregation was never mandated by law. Here, the fact that the DISD practiced de jure segregation in the past was established decades ago; the question is whether any current segregated condition may be attributed to the earlier constitutional violation. In Swann v. Board of Education, 402 U.S. 1, 91 S.Ct. 1267, 28 L.Ed.2d 554 (1971), the Supreme Court stated unequivocally that
[wjhere the school authority’s proposed plan for conversion from a dual to a unitary system contemplates the continued existence of some schools that are all or predominately of one race, they have the burden of showing that such school assignments are genuinely nondiscriminatory. The court should scrutinize such schools, and the burden upon the school authorities will be to satisfy the court that their racial composition is not the result of present or past discriminatory action on their part.
Id. at 26, 91 S.Ct. at 1281. Accord, Dayton Board of Education v. Brinkman (Dayton II), 443 U.S. 526, 537, 99 S.Ct. 2971, 2978, 61 L.Ed.2d 720 (1979); Keyes, 413 U.S. at 211, 93 S.Ct. at 2698. We should not have to explain at this late date who has the burden of proving that a current condition of racial segregation is not a vestige of the past.
The district court’s findings with respect to the continued existence of vestiges of past segregation within the DISD are not entirely clear. There are points in the district court’s opinion in which the court suggests that
with respect to the few remaining predominantly anglo schools and with respect to many of the predominantly minority schools ... the relationship between past segregative acts and present segregation has “become so attenuated as to be incapable of supporting a finding of de jure segregation warranting judicial intervention.”
520 F.Supp. at 707 (quoting Keyes v. School District No. 1, 413 U.S. 189, 211, 93 S.Ct. 2686, 2698, 37 L.Ed.2d 548 (1973)). “[U]nable to discern from the decisions of the higher federal courts any guidelines by which to determine when such an ‘attenuated’ status has been reached,” however, and “in view of the remedy being prescribed,” the court saw “no reason to pioneer this field.” Id. The court also concluded that at least some vestiges continued to exist within the DISD:
[Vjestiges of past segregation continue to exist in DISD, evidenced by some of the predominantly minority schools, the specific number and exact identity of which the Court cannot determine and further evidenced, to an unascertainable extent, by the lower achievement of minority students as compared to anglo students, as reflected by objective testing.
Id. This conclusion was essentially based on the DISD’s failure sufficiently to rebut, in these proceedings held pursuant to our mandate, the Swann presumption that one-race schools in a school system with a history of de jure segregation are vestiges of the past:
Keyes [sic] mandates a finding that vestiges of the previous segregated system remain today, even though diminished and attenuated by the very passage of time and by the absence since 1971 of any intentional discriminatory motives or conduct (other than as presumed by Keyes [sic] ).
*95DISD vigorously asserts that nearly all of the current predominantly minority schools are due to the increase in minority student population, or to residential patterns and developments which have occurred completely unrelated to any acts or omissions of DISD. This argument may well be true with respect to many of those schools but the Court could not conclusively so find without additional evidence.
Id. at 706.
The district court’s findings must be read in the context of our prior mandate. We expressly remanded the case to the district court “for the formulation of a new student assignment plan,” and specified that “[t]he district court is directed to include in its plan a majority-to-minority transfer option with adequate transportation.” Tasby II, 572 F.2d at 1018. With respect to the student assignment plan, we directed the court to make “findings to justify the maintenance of any one-race schools that may be a part of that plan.” Id. As to other aspects of the district court’s previous order, we required that court “to reassess such provisions in light of the remedy it fashions with respect to school assignments” and to “consider the feasibility of desegregating the new complex.” Id. Plainly, our mandate contemplated and required the formulation of desegregation remedies, as distinguished from a determination whether the school district should be subject to any court desegregation supervision or orders. Compare Tasby III, 520 F.Supp. 683 with Price v. Denison Independent School District, 694 F.2d 334, 366-68 (5th Cir.1982) (where lawsuit challenging student assignment plan was filed fourteen years after court had ordered desegregation plan, district court was required to make findings whether and to what extent schools were currently segregated, and whether any current segregation was a vestige of the prior de jure segregated school system). The determination that the DISD should be subject to court supervision had already been made in 1976. The hearing below, held in compliance with our mandate, was essentially completed just sixteen months after the case had returned to the district court upon the Supreme Court’s dismissal of certiorari in Tasby II.
As we understand the district court’s opinion, taken as a whole, the court concluded that there was insufficient evidence in the record that the vestiges found by Judge Taylor to exist in 1976 had been so obliterated as to authorize a departure from the express requirements of our prior mandate when there were still portions of the DISD amenable to further desegregation remedies. Our review of the record in this case does not indicate that the court erred in reaching this conclusion. For example, Dr. Wright, the DISD superintendent, suggested that the current racial segregation in the schools was the result of housing patterns that would have been the same even without the existence of a de jure school system in the 1950s and 1960s. He admitted, however, that the imposition of a de jure system could have been one of the causes of those housing patterns. 12 Record at 245.
The district court also mentioned the “lower achievement of minority students as compared to anglo students” in its conclusion that vestiges of past segregation continue to exist in the DISD. 520 F.Supp. at 707. We do not understand the court to have found that the achievement disparity that continued to exist in 1981 was necessarily attributable to the dual school system. There was no need for such a finding because the parties had agreed that the DISD would implement programmatic remedies in predominately minority schools. See Milliken v. Bradley (Milliken II), 433 U.S. 267, 286 n. 17, 97 S.Ct. 2749, 2760 n. 17, 53 L.Ed.2d 745 (1977) (“it must always be shown that the constitutional violation caused the condition for which remedial programs are mandated") (emphasis added). In fact, at oral argument, counsel for the NAACP explained that he had been prepared to put on evidence of the relationship between the present achievement disparity and the prior de jure segregated school system, but he had decided not to do *96so when the DISD agreed to institute programmatic remedies in all predominately minority schools.
In essence, the court’s statement with respect to the continuing achievement disparity was based upon Judge Taylor’s earlier findings. We note that most of the students now enrolled in the schools entered the school system after the DISD had begun to comply with the court-ordered desegregation plans. When the time comes for the district court again to determine whether the school system is unitary, as it must eventually, it should carefully consider whether any continuing achievement disparity between students can still be attributed to the de jure school system.
Under the circumstances of this case, we do not believe that the district court was required to, nor do we believe that it purported to, make a new definitive determination respecting the non-unitary status of the school district before or concurrently with making the determinations and orders expressly required by our prior mandate. Doubtless some dramatic and extensive change in conditions would have excused the district court from compliance with our mandate.7 The district court determined that such a change had not been demonstrated. It is in this limited context, as well as in the context of the parties’ agreements as to remedies, that the district court’s references to low achievement of minority students, its inability to “conclusively” find unitary status “without additional evidence,” and the lack of “guidelines” from “higher federal courts,” must be understood. The district court determined that it was not excused from compliance with our mandate, but it did not definitively determine that the school district was not unitary in 1981. As noted, Judge Taylor did definitively make such a determination in 1976.
The time will come when the issue of unitariness must be addressed again, on its own merits. While in significant measure the timing is within the discretion of the district court, certainly such a determination cannot be indefinitely postponed.8 When it is made, the issue must be addressed fully and directly, free of any constraint that the district court’s judgment here, or our affirmance of it, constitutes a law of the case (or res judicata) determination that the school district was not unitary during or after 1981. Moreover, while the burden will certainly be on the school district, there will be no requirement that unitary status, or matters relevant thereto, be proved or found “conclusively.” The fact-finding process may be difficult, but it may not be bypassed. See Price, supra, 694 F.2d at 366-68. Our decision in Ross will presumably be helpful in providing guidance for making the required determinations in such a proceeding.
III. COURT-ORDERED REMEDIES.
In reviewing the propriety of the court-ordered relief in this case, it is important to remember that most of what constituted the court’s judgment was agreed to by the parties and is not challenged on *97appeal.9 Further, our review of the trial court’s desegregation remedy is limited to ascertaining whether the court abused its discretion. Valley v. Rapides Parish School Board (Valley II), 702 F.2d 1221, 1225 (5th Cir.1983) (citing Milliken v. Bradley (Milliken II), 433 U.S. 267, 288, 97 S.Ct. 2749, 2761, 53 L.Ed.2d 745 (1977)). The trial court’s “task is to correct, by a balancing of the individual and collective interests, the condition that offends the Constitution.” Swann, supra, 402 U.S. at 16, 91 S.Ct. at 1276. “The criterion for determining the validity of provisions in a desegregation plan is whether they are reasonably related to the ultimate objective.” Valley v. Rap-ides Parish School Board (Valley I), 646 F.2d 925, 938 (5th Cir.1981).
A. The Minority Neighborhood Option Plan.
The appellants complain that the district court failed to exercise its discretion in rejecting the MNOP plan for the 4-8 centers because it believed that approval of the plan would be beyond the scope of our remand. We do not agree with this contention. The district court properly considered the fact that the MNOP plan would increase the number of predominately one-race schools, and that our earlier opinion expressed a concern about the already substantial number of such schools, while we were satisfied with the remedies to be implemented for the 4-8 centers.
The court engaged in an analysis of the relative interests on both sides of the issue and concluded that the equities in the case militated against a court-ordered MNOP plan. The court was sensitive to the Black Coalition members’ desire for neighborhood schools, but it noted that many of the black parents objected to mandatory transportation because the burdens had been disproportionately placed on minority children and not out of any rejection of the constitutional principles set forth in Brown v. Board of Education (Brown I), 347 U.S. 483, 74 S.Ct. 686, 98 L.Ed. 873 (1954). The court was concerned that the MNOP plan would disrupt a desegregation plan that had been in place for five years and that it would resegregate schools that had been successfully desegregated. Unable to reconcile the resegregative aspects of the MNOP plan with traditional constitutional principles favoring maximum desegregation, see Swann, supra, 402 U.S. at 26, 91 S.Ct. at 1281; Lee v. Macon County Board of Education, 616 F.2d 805, 808-09 (5th Cir.1980), the court concluded that adoption of such a plan would be inappropriate at this time.
Under these circumstances, where our remand found nothing specifically wrong with the 4-8 centers, and where the proposed plan had a significant prospect of resegregating already successfully desegregated schools, we cannot say that the court’s refusal to order such a plan was an abuse of discretion, particularly in light of the fact that the minority parents have not appealed the court’s rejection of their plan. We express no opinion, however, on whether a school district, not subject to a court-ordered desegregation plan, could lawfully adopt such a plan.
B. Alteration of Attendance Zones.
Swann requires close scrutiny of one-race or “predominately” one-race schools “to determine that school assignments are not part of state-enforced segregation.” 402 U.S. at 26, 91 S.Ct. at 1281.10 The district *98judge was especially concerned with the continued existence of predominately anglo schools11 because of their potential to create a “perception by minority children that they are excluded from a school because of their race.” 520 F.Supp. at 716.12 Therefore, he asked for suggestions about the feasibility of obtaining further desegregation of these schools. He expressed particular interest in W.T. White, Hillcrest and Bryan Adams High Schools,13 and Lagow and Mosely K-3 schools. The court stated, however, that “[a]ny proposed attendance zone changes should conform to the limitations of time and distance imposed by [its] Opinion, and should not disturb the status of already desegregated schools.” Id. at 750. The plaintiffs proposed alterations in the attendance zones of some of the naturally integrated areas contiguous to these schools, and the court accepted their proposal. The appellants object to the reassignment of students in East Dallas from Woodrow Wilson High School and the J.L. Long Middle School feeder zone to Bryan Adams High School and W.H. Gaston Middle School, and to the reassignment of students in North Dallas from Cary Middle School and Thomas Jefferson High School to W.T. White High School and Marsh Middle School.
We agree with the appellants that the reassignment of students in East Dallas was an abuse of discretion because it was not reasonably related to the ultimate objective. See Valley I, supra. The district court’s own opinion illustrates why the plaintiffs’ East Dallas proposal should not have been accepted. As the court recognized, Woodrow Wilson and its 4-8 feeder school are naturally desegregated schools; hence, they should have been left undisturbed if possible. 520 F.Supp. at 705, 716; see also Milliken II, 433 U.S. at 288 n. 19, 97 S.Ct. at 2761 n. 19; Tasby v. Estes, 412 F.Supp. 1192, 1206 (N.D.Tex.1975). The court agreed, however, to disturb these schools to desegregate further a school that was less than a percentage point over the predominately one-race standard, and which was expected to desegregate naturally by 1982. 520 F.Supp. at 734. As of October, 1981, Bryan Adams had a 75.33% anglo population; that population was expected to drop below 75% by 1982.
The appellees contend that the East Dallas alteration was not an abuse of discretion because it was so insignificant. Numerically, the change, which involves the transfer of some 120 students in a school system containing hundreds of thousands, is indeed minor. It is precisely because the numerical change on the desegregation side of the balance sheet is so small, however, that the major symbolic importance of the change to the naturally desegregated area cannot be justified. No one disputes the idea that a *99naturally desegregated school provides the greatest promise of successful and stable integration. To disturb that process for a change in a few percentage points in a school that would itself naturally desegregate within a year anyway is an abuse of the district court’s remedial discretion.
We understand the trial court’s dilemma and frustration in this case. Like the courts in Atlanta and Houston, it was confronted with a school system in which the traditional desegregation tools could not be used to eliminate the continued existence of predominately one-race schools, and thus it concluded that it should do whatever time and distance factors allowed. But as the district court itself recognized, time and distance factors are not the only considerations. See Estes v. Metropolitan Branches of the Dallas NAACP, 444 U.S. 437, 444, 100 S.Ct. 716, 719, 62 L.Ed.2d 626 (1980) (Powell, J., dissenting from the dismissal of certiorari). While the fear of white flight cannot be accepted as a reason for not acting, United States v. Scotland Neck City Board of Education, 407 U.S. 484, 491, 92 S.Ct. 2214, 2218, 33 L.Ed.2d 75 (1972), the court may elect a constitutionally permissible plan “calculated to minimize white boycotts.” Stout v. Jefferson County Board of Education, 537 F.2d 800, 802 (5th Cir.1976). Because we conclude that it would have been constitutionally permissible to let Bryan Adams desegregate naturally, in light of the fact that it was already almost desegregated and would drop below the “magic number” in the near future, we hold that the alteration of the Woodrow Wilson and J.L. Long Middle School feeder zones to achieve “desegregation” one year early was an abuse of the trial court’s discretion.
The North Dallas alteration presents a different case. The 1981 enrollment in W.T. White High School was 82.87% anglo, and the percentage of anglo students was not expected to drop below the seventy-five percent standard within the next five years. While a naturally integrated school should not be disturbed if possible, the DISD concedes that such schools are not “sacrosanct enclaves” that may never be included in a desegregation plan. We hold that the district court did not abuse its discretion in transferring a small number of students out of naturally desegregated Thomas Jefferson High School to integrate further W.T. White High School, since W.T. White showed no sign of becoming integrated on its own in the near future. Similarly, there was no abuse in the alteration of attendance zones for the two middle schools.
G. Minority Personnel Goals.
The Curry intervenors, representing “a group of far North Dallas parents and students,” 520 F.Supp. at 689, are the only parties who have challenged the district court’s revision of the 1976 minority hiring goals.14 In fact, the DISD informed us at oral argument that it could “live with” the new goals. No one challenged the district court’s authority in 1976 to set minority hiring goals in an attempt to disestablish the faculty assignment portion of the prior dual school system. It was equally within the court’s authority to modify those hiring goals at some future date as a part of its overall desegregation plan formulated in compliance with the directions of this court’s mandate. See United States v. Montgomery Board of Education, 395 U.S. 225, 233, 89 S.Ct. 1670, 1674, 23 L.Ed.2d 263 (1969) (approving district court faculty desegregation plan that established numerical goals and provided that goals for future years were reserved for later decision).
The intervenors have also expressed a concern that the hiring goals are not attainable, and they maintain that the court’s *100personnel remedy has not been carefully tailored to fit the violation. See Milliken II, 433 U.S. at 282, 97 S.Ct. at 2758. The intervenors have offered no support for their suggestion that the court’s remedy exceeds the scope of its remedial powers. In light of the DISD’s statement that it can “live with” the new goals, we do not share the intervenors’ concern about the feasibility or propriety of the remedy. We emphasize that the district court’s order sets goals, not quotas. In the absence of any indication of how the new goals will unnecessarily trammel anyone’s rights and in light of the DISD’s own statement that the goals are feasible, we conclude that the district court’s revision of the minority hiring goals was not an abuse of discretion.
IV. CONCLUSION.
We hold that the district court did not err in failing to declare, for the purposes of these particular proceedings, that the DISD had achieved unitary status in light of the court’s determination that further remedial measures were feasible and in the absence of convincing evidence that conditions had sufficiently changed so as to authorize a departure from this court’s mandate. We hold further that the court did not abuse its discretion in rejecting the MNOP plan, in revising the minority hiring goals, or in altering the North Dallas attendance zones, but that its alteration of the East Dallas attendance zones was an abuse of discretion.
The appellants shall bear the costs of this appeal. AFFIRMED in part; REVERSED in part.
. The Dallas Independent School District has been a party to desegregation litigation for a much longer period of time. The first challenge to the constitutionality of the Dallas school system was filed shortly after the Supreme Court’s second decision in Brown v. Board of Educ. (Brown II), 349 U.S. 294, 75 S.Ct. 753, 99 L.Ed. 1083 (1955). See Bell v. Rippy, 133 F.Supp. 811 (N.D.Tex.1955).
. Throughout this litigation, we have defined as a “one-race school” any school that has a student body with “approximately 90% or more students being either anglo or combined minority races.” Tasby II, 572 F.2d at 1012 n. 3.
. When this lawsuit was filed, the total enrollment in the DISD was 58.2% anglo, 33.4% black, and 8.4% hispanic. During the intervening decade, the anglo enrollment in the DISD has dropped precipitously while hispanic enrollment has increased dramatically; black enrollment has also shown some increase. As of 1981, the ethnic composition of the district was 29.53% anglo, 49.61% black, and 19.44% his-panic. 520 F.Supp. at 693. Anglos still constitute a majority, however, of the people residing in the district. Id. at 694.
. While the Curry intervenors did not sign the stipulation, they have not objected to its contents on appeal.
. As of 1981, there were three predominately anglo high schools — W.T. White, Bryan Adams and Hillcrest — and a number of predominately anglo K-3 schools, including Lagow and Mosely. 520 F.Supp. at 750.
. The DISD relied on the Curry intervenors to make the argument that the school system is now unitary.
. Compliance with an appellate court’s mandate is normally required by the doctrine of law of the case; the district court may disobey the mandate only where “[1] the evidence on a subsequent trial [is] substantially different, [2] controlling authority has since made a contrary decision of the law applicable to such issues, or [3] the decision was clearly erroneous and would work manifest injustice.” Morrow v. Dillard, 580 F.2d 1284, 1290 (5th Cir.1978) (quoting White v. Murtha, 377 F.2d 428, 432 (5th Cir.1967)); accord United States v. Texas Educ. Agency, 647 F.2d 504, 506 (5th Cir.1981), cert. denied, 454 U.S. 1143, 102 S.Ct. 1002, 71 L.Ed.2d 295 (1982); Schwartz F only one of these three exceptions that is even arguably applicable here is the first, but even it was not established. The defendants failed to show that the change in circumstances was so substantial as to justify disregard of our prior mandate.
. Some of the remedies prescribed by the district court and the parties in this case are not scheduled to be completed until 1987. Our affirmance of the district court’s judgment does not preclude that court from making a determination of the DISD’s unitary status prior to the substantially complete implementation of the present plan.
. For example, no one challenges the propriety of the DISD’s agreement to provide programmatic remedies to minority students in predominately minority schools. See Milliken II, supra, 433 U.S. at 286 n. 17, 97 S.Ct. at 2760 n. 17.
. The district court defined a “one-race school” as a school that “has a student body with approximately 90% or more of the students being either of anglo or combined minority races,” 520 F.Supp. at 707, and a “predominately one-race school” as a school with a 75%/25% racial ratio. Id at 711. The court borrowed the 75%/25% standard from its earlier definition of a naturally integrated school and noted that it was the measure of a racially identifiable school used by Justice Powell in his dissent from the dismissal of certiorari in the appeal from our earlier opinion, Estes v. Metropolitan Branches of the Dallas NAACP, 444 U.S. 437, 442, 100 S.Ct. 716, 718, 62 L.Ed.2d 626 (1980). 520 F.Supp. at 709 n. 57. The *98district court noted further that the parties on both sides of this litigation had used the 70-75% figure as a measure of a desegregated environment and that
there is a basis for this standard in experience and common sense, as borne out by the pertinent social science literature. Research by various experts indicates that for effective participation and healthy interpersonal interaction among students, an ethnic or racial group in the numerical minority should ordinarily comprise at least 20% of the student body. Twenty-five percent gives a group a “presence” in a school, and is a sufficient number to form an effective bloc. Also, when historical trends are examined it appears that once a school, which had previously been virtually all-anglo, attains a 25% minority representation, it is very likely that this percentage representation will increase, rather than stay constant or decrease.
Id. at 712. (footnotes omitted). Since neither side has objected to the use of the 75%/25% standard, we will assume for the purposes of this appeal that that standard is the appropriate measure of a predominately one-race school.
. The court found that the DISD had “virtually eliminated one-race anglo schools.” 520 F.Supp. at 709.
. We note that no one has appealed the present plan’s failure to eliminate the substantial number of one-race minority and predominately one-race minority schools that continue to exist throughout the district.
. As of October, 1981, W.T. White’s enrollment was 82.87% anglo, Hillcrest’s was 74.20% anglo, and Bryan Adams’ was 75.33% anglo. See DISD Report to the Court, December 15, 1981, Appendix A.
. In 1976, the district court directed the DISD to “develop recruiting and employment policies to insure that competent personnel are employed and that by 1979-80 the percentages of Black and Mexican-American personnel approximate the percentages at a minimum of 31% Black and 8% Mexican-American.”F1982, the district court updated the minority hiring goals for the DISD to reflect changes in the ethnic population of the school district. The court revised its judgment to provide that “blacks and hispanics should represent at a minimum 43% and 12%, respectively, of all DISD teacher positions by the 1986-87 school year.” 10 Record at 2036.