On these appeals, defendants-appellants City of Yonkers and Yonkers Community Development Agency (collectively, "the City") appeal from two orders entered January 30, 1987 and March 17, 1988 in the United States District Court for the Southern District of New York (Sand, J.), which direct the City to provide funding for the construction of two new schools in accordance with the public school desegregation plan approved in that court's prior School Remedy Order. Because the City's objections to the construction of these schools clearly were encompassed in its prior appeal to this Court and present no new issues, we hold that their resolution has become the law of the case and decline to reconsider them. Therefore, we affirm the orders of the district court.

In United States v. Yonkers Bd. of Educ., 837 F.2d 1181 (2d Cir.1987), cert. denied, --- U.S. ----, 108 S. Ct. 2821, 100 L. Ed. 2d 922 (1988), familiarity with which is assumed, this Court affirmed a judgment of the United States District Court for the Southern District of New York (Sand, J.), see 624 F. Supp. 1276 (S.D.N.Y.1985), that held, inter alia, defendants the City and Yonkers Board of Education ("the Board") liable for racial segregation of Yonkers public schools and directed them to undertake measures to remedy that segregation. This Court also affirmed three subsequent remedial orders issued by the district court, including a School Remedy Order entered May 13, 1986, see 635 F. Supp. 1538 (S.D.N.Y.1986).

The School Remedy Order was issued following the submission of two proposed remedial plans by the Board and responses by the government and plaintiffs-intervenors NAACP. The plan adopted in the order included provisions for school closings, dedicated and attendance-area magnet schools, a voluntary student transfer program, and the appointment of a Monitor "empowered to make recommendations to the Court with respect to changes she/he believes necessary to make the plan more effective," id. at 1552. The plan required, inter alia, the construction of two new schools: (1) a new "attendance area magnet" elementary school to replace School 19, see id. at 1542-43; and (2) the Hudson River Museum Junior High School ("the Museum School"), one of four nonattendance zone, dedicated magnet schools designed "to reduce racial/ethnic isolation by attracting students to programs that emphasize areas of special interest," id. at 1541, in this instance, a program for gifted and talented students. Finally, the district court "anticipated that the necessary funding [for implementing the plan] will be provided by the City of Yonkers," id. at 1551.

In the second order, issued on May 28, 1986, the district court directed that "[t]he City shall ... provide funding for all of the school desegregation measures required by" the School Remedy Order, 635 F. Supp. 1577, 1583 (S.D.N.Y.1986) (the "Housing Remedy Order").

On July 1, 1986, the district court issued the third order, requiring the City to fund the operating and capital expenses of the first year of the desegregation plan. This order originated in the City's June 11, 1986 motion for a stay of the remedy orders on the ground that the cost of the schools was neither related to desegregation nor accurately estimated. Although this motion was denied, the district court allowed the City to submit evidence on the issue whether some items in the Board's budget were not required for desegregation purposes. The City accordingly submitted, inter alia, a report prepared by the Bennett, Keilson & Co. accounting firm. The Bennett Report "concluded that the School District has substantially underestimated the cost of the two proposed schools" and "[f]rom a financial standpoint and based on the limited information provided," questioned the need for any new school construction "since there is no need to change the overall capacity of the district," Joint App. at 173-74. The Museum School cost was deemed "difficult to justify in light of existing capacity in the district," including the Walt Whitman School, id. at 174. The "substantial rehabilitation" of School 19 was found "significantly less expensive without impacting the objectives of the desegregation plan," id., although the Report made no estimate of rehabilitation cost. The Bennett Report was referred to the Monitor, who found in his July 15 report that the schools were necessary and recommended that the Board proceed with their planning.

On July 10, 1986, the City filed notices of appeal from Judge Sand's School and Housing Remedy orders of May 13, May 28, and July 1, 1986. On December 28, 1987, this Court rejected the City's position and upheld the district court's liability judgment and remedy orders in full. See 837 F.2d at 1237-39.

During the pendency of the prior appeal, the City moved on December 15, 1986 to modify the School and Housing Remedy Orders insofar as they required the City to fund the development and construction of School 19 and the Museum School. The City argued that: (1) the expenses for the two schools were not related to desegregation and thus the court had no authority to order their construction; (2) the Museum School was unnecessary; and (3) creation of a smaller, "new or different" magnet program in a rehabilitated School 19 was less costly than, but equally effective as, construction of a new school. Following oral argument, Judge Sand denied the motion, noting that the Board "had originally proposed these two new schools and no party raised any objection to their construction prior to the entry of the" School Remedy Order, Joint App. at 207 (Order of Jan. 30, 1987). He directed the Board "to determine," for submission to the Monitor, "the cost, feasibility and consistency with the integrative objective of the [School] [R]emedy [O]rder of rehabilitating the current [S]chool 19 and placing thereat the magnet program contemplated for the new [S]chool 19" in addition to "commenc[ing] immediately all ... planning steps necessary for the construction of these new schools," id. at 207-08.

The court modified the School Remedy Order on March 13, 1987 pursuant to an agreement reached by the parties that eliminated the planned relocation of the Saunders School and the Burroughs Junior High School. This modification did not change the relative geographic distribution of the plan: One permanent secondary school (Burroughs) remained in the Southwest, two remained in the Southeast and Northeast, and three remained in the Northwest.

The Monitor issued his Report and Recommendation on proposals concerning a new School 19 and the Museum School on August 26, 1987. He found that rehabilitating School 19 to accommodate the planned magnet program would cost $500,000 more than constructing a new school on a new site. See Joint App. at 430. The Monitor rejected the City's proposal to close School 19 altogether and reassign its students to other schools because it would "impose an undue burden on the minority children the remedial order is intended to serve," id. at 431. The City's proposal to renovate School 19 to accommodate a different magnet program of smaller enrollment was rejected because the ability of the magnet program to attract nonminority students to Southwest Yonkers would be crucial to its effectiveness. Id. at 432. The Monitor concluded that because the burden to attract nonminority students to the area "is clearly upon the Board, not the City," the Board must have "reasonable freedom" to design an effective program. Id.

The Monitor also rejected the City's contention that the proposed site for the Museum School was "intended for other developmental purposes" creating "economic, contractual and legislative impediments surrounding" its acquisition, since it required only three acres and could be developed consonantly with the other proposed uses. See id. at 433. The City's suggestion that the Museum School could be "accommodated through an expanded School # 25 and the use of School # 6" was rejected as "unworkable," id., because School 6 "is located on a difficult site, is antiquated (in part) beyond cost-effective rehabilitation, and the need to acquire adjacent sites poses likely time and cost constraints," id. at 433-34. Accordingly, the Monitor recommended that: (1) the court order the immediate funding for a new School 19; (2) the City and the Board attempt to agree on a site for the Museum School; and (3) the Board work to reduce the estimated cost of the Museum School. Id. at 434-35.

The City filed objections to the Monitor's Report and Recommendations on September 16, 1987. The City questioned the need for, and the efficacy of, the Board's planned magnet program for School 19, Joint App. at 224-26, and argued that the proposed Museum School was not justifiable as desegregation-related because it would " 'skim[ ]' off students who would otherwise attend regular schools in a heterogeneous fashion," id. at 239. The Board responded with reports from the district's Assistant Superintendent and its desegregation expert, Dr. Rossell, countering the City's claims.

On January 11, 1988, the Monitor issued a second Report and Recommendation recommending the construction of both new schools. The Monitor observed that "[a]mong all of the questions posed to [him], none is more easily answered than that which questions the need for a new School # 19," id. at 308. He found that: (1) present School 19 had 92% minority enrollment; (2) "[a]mple evidence" demonstrated that the 80 year-old facility was in an "undesirable condition to serve as an effective elementary school and to afford equal educational opportunity"; and (3) the present location was undesirable due to its physical limitations and the unacceptable social conditions of the neighborhood. As for a "rehabilitated" School 19 with smaller capacity, the Monitor found that it would be expensive, less cost effective, and fraught with all those problems currently posed by the neighborhood. Furthermore, the Monitor concluded, restoration would impose "a burden on more minority students who must leave the school than if its current capacity remained," id. at 310.

The Monitor also reiterated his original conclusion that the Museum School was necessary to the desegregation plan, citing among other reasons the need to provide "a viable and visible gifted and talented program for both majority and minority students," to "attract and retain majority students at the junior high school level where preliminary data point to measurable attrition," and to "meet the equal educational opportunity standard," id. at 327-28. In addition to steps toward compliance with the orders similar to those he had recommended previously, the Monitor now recommended that the court require the City to fund School 19 within 30 days and allow the City the option to substitute its alternative site for School 19.

On February 3, 1988, the district court approved and adopted each of the Reports and Recommendations and entered an order on March 17 directing the City to provide funding for both proposed schools. The City now appeals from the January 30, 1987 and March 17, 1988 orders and raises here the same objections made before the district court.

The doctrine of law of the case "posits that when a court decides upon a rule of law, that decision should continue to govern the same issues in subsequent stages in the same case." Arizona v. California, 460 U.S. 605, 618, 103 S. Ct. 1382, 1391, 75 L. Ed. 2d 318 (1983); United States v. Melendez-Carrion, 820 F.2d 56, 60 n. 1 (2d Cir.1987). Law of the case requires "adherence by an appellate court to its own decision at an earlier stage of the litigation," United States v. Cirami, 563 F.2d 26, 33 n. 6 (2d Cir.1977), and applies both to that which is expressly decided "as well [as] to everything decided by necessary implication," Fogel v. Chestnutt, 668 F.2d 100, 108 (2d Cir.1981), cert. denied sub nom. Currier v. Fogel, 459 U.S. 828, 103 S. Ct. 65, 74 L. Ed. 2d 66 (1982). Although "a discretionary doctrine which 'does not constitute a limitation on the court's power but merely expresses the general practice of refusing to reopen what has been decided,' " United States v. Birney, 686 F.2d 102, 107 (2d Cir.1982) (quoting Slotkin v. Citizens Cas. Co., 614 F.2d 301, 312 (2d Cir.1979), cert. denied, 449 U.S. 981, 101 S. Ct. 395, 66 L. Ed. 2d 243 (1980)), law of the case will be followed "absent 'cogent' or 'compelling' reasons," Doe v. New York City Dep't of Soc. Servs., 709 F.2d 782, 789 (2d Cir.), cert. denied sub nom. Catholic Home Bureau v. Doe, 464 U.S. 864, 104 S. Ct. 195, 78 L. Ed. 2d 171 (1983). It is not enough for the party seeking consideration to make a more persuasive argument. See Fogel, 668 F.2d at 109. There must be " 'an intervening change of controlling law, the availability of new evidence, or the need to correct a clear error or prevent manifest injustice.' " Doe, 709 F.2d at 789 (quoting 18 C. Wright, A. Miller & E. Cooper, Federal Practice and Procedure Sec. 4478, at 790 (1981) (footnote omitted)); Melendez-Carrion, 820 F.2d at 60 n. 1.

Both School 19 and the Museum School were part of the School Remedy Order, the May 28, 1986 order and the July 1, 1986 order that this Court "in all respects affirmed," 837 F.2d at 1239. We rejected the City's arguments that not all of the elements of the desegregation plan were necessary to remedy the violations:

The voluntary magnet-school plan was adopted only after all of the parties had been given an opportunity to submit proposals.... The court ... has taken care to ensure that the Board's projected expenditures ... are in furtherance of the desegregation remedy rather than of the general enrichment of the school program.... The City, though given an extra opportunity to do so, did not show that any part of the adopted plan was duplicative or unnecessary to the plan's success.

Id. (emphasis added). Although the two orders at issue here had not been entered at the time the prior appeal was taken, they do no more than enforce what the district court previously had ordered.

There is no dispute that the Museum School was, and is, a part of the plan that we previously affirmed. However, the City contends that the consensual modification of the plan, eliminating the relocation of the Saunders School and the Burroughs Junior High School, "radically changed the facility utilization originally approved in the" School Remedy Order, Appellant's Brief at 4, thereby creating grounds for our review of the merits of the Museum School proposal. We reject this contention. The modification did not alter the original scheme of the plan to have only one operating junior high school in Southwest Yonkers. We therefore do not view the modification as an appropriate ground for re-examining the necessity of the Museum School.

The City's objections to a new School 19 are based on a dispute over the relative costs of building a new facility rather than rehabilitating the existing one. However, in the previous appeal this Court expressly found that

the district court plainly made appropriate efforts to eliminate any expense that was not necessary to remedy the violations found and to minimize the degree to which the remedy would interfere with the autonomy of the City and the Board.... The court required the Board to submit a separate itemized budget for the desegregation expenses; it made appropriate findings that the proposed budget represented the reasonable and necessary estimated cost of implementing the plan; and it has taken care to ensure that the Board's projected expenditures for the ordered plan, insofar as they exceed the normal budgetary appropriations, are in furtherance of the desegregation remedy....

837 F.2d at 1239. Moreover, in rejecting "the City's complaint that it is improperly being required to pay for a desegregation plan that is more expensive than a simple mandatory busing plan would be," id. at 1238, we concluded that "[a]lthough there is no question that the court-ordered plan is more expensive, that simple fact provides no basis for altering the relief ordered," id., and we affirmed the district court's exercise of discretion to require the City to fund the plan, id. at 1239. The City's instant argument--that construction cannot be ordered where renovation is less expensive--is a mere variation on the basic contention it raised previously--that it should be ordered to fund only the least costly "effective" remedy. We clearly rejected that position in our prior decision, and the rule stated there is binding on the City as to this aspect of the plan as well.

Because the City's appeal presents no issues that were not decided in, nor necessary to the decision of, the prior appeal, we hold that the propriety of ordering the City to fund construction of School 19 and the Museum School has become the law of the case. Accordingly, we affirm the orders of the district court.