ALVIN B. RUBIN, Circuit Judge:

In 1956, two years after the Supreme Court decided Brown v. Topeka Board of Education, 347 U.S. 483, 74 S.Ct. 686, 98 L.Ed.2d 873 (1954) (Brown I), a group of parents of black children enrolled in the Houston Independent School District (HISD) filed this suit to desegregate its schools. After twenty-five years of court proceedings and twelve years of operation under a court-ordered desegregation plan, the district court has now decided that the school district has eliminated all vestiges of de jure segregation and has become unitary. The vestiges of all discriminatory practices have been eliminated in every aspect of school operations, but efforts at integration have failed in one aspect alone: the district has not achieved integrated student attendance. The district court found, however, that the homogeneous student composition of the schools does not stem from the unconstitutional segregation practiced in the past but from population changes that have occurred since this litigation commenced, and that the geography of the school district, traffic conditions, and population patterns make further efforts to eliminate all one-race schools impractical.

The district court found that HISD has eliminated the vestiges of state-imposed segregation within the boundaries of this large and sprawling school district, whose black and Hispanic population increases annually while its white population dwindles, although desegregation has provided an integrated learning environment for few of the successors of the black children who originally brought this action. We conclude that the district judge did not err in deciding that lack of effort does not account for the student attendance patterns in HISD. Because that court's findings of fact are not clearly erroneous and its decision is supported by the record, we affirm.

The district court also denied the plaintiffs-appellants leave to amend the complaint so as to add twenty-six additional parties and seek interdistrict relief from both the HISD and adjacent school districts, not previously parties to the suit, on the ground that the new claim came too late to be considered in this proceeding. We affirm that action without prejudice to the assertion of such a claim in an appropriate suit.

I.

HISD is now the fifth largest school district in the nation. During the 1978-79 school year, 201,960 students enrolled in its 226 schools — 170 elementary, 34 junior high, and 22 senior high schools. It is one of nine school districts located in the city of Houston and one of twenty districts in Harris County. Defined by statute long before Brown I, its boundaries meander in and out of Houston's city limits. Three of the school districts serving Harris County also include territory in adjoining counties and three more districts serving students in the metropolitan area are wholly or in large part outside Harris County, but directly south of and adjacent to HISD. In 1978-79, HISD's students were 36% of the total student population served by HISD and the eleven surrounding school districts; however, 71% of the area's black and 60% of the area's Hispanic students were enrolled in HISD schools.

During the twelve years since 1970 when the first desegregation plan took effect, residential segregation within the district has increased dramatically. In addition, there have been major changes in the population of the district. While the number of black families has increased only moderately, white families have moved from the district and Hispanic families have moved into it. In most instances, black neighborhoods remain adjacent to Hispanic neighborhoods.

Concomitant with these demographic changes, the ethnic composition of the student population has changed. Sixteen schools that in 1970 were at least 90% white, for example, have now become at least 90% black. During the 1969-70 school year, the student population was 53.1% white, 33.5% black, and 13.4% Hispanic. By 1978-79, the percentages had changed to 30.8% white, 45% black, and 24.2% Hispanic. In the 1981-82 school year, 26% of the HISD student population was white; 74% was black and Hispanic. By 1985-86, according to 1979 projections, enrollment will be 20% white, 38% black, and 42% Hispanic.

Desegregation of HISD began in February 1956 when a group of black parents and students filed a complaint charging that the district and its officers were operating a dual public school system by means of overlapping racially segregated attendance zones. In November 1957, the district court entered an order declaring void certain Texas civil statutes that had fostered the dual system and restraining and enjoining defendants from requiring segregation. Ross v. Rogers, 2 Race Rel.L.Rep. 1114 (S.D.Tex. 1957). Three years later the district court ordered implementation of a grade-per-year voluntary transfer plan by which black or white students could elect to enter the school within their attendance zone which served the other race. No separate provision was made for Hispanics. Ross v. Peterson, 5 Race Rel.L.Rep. 703, 709 (S.D. Tex.), aff'd sub nom. Houston Indep. School Dist. v. Ross, 282 F.2d 95 (5th Cir.), cert. denied, 364 U.S. 803, 81 S.Ct. 27, 5 L.Ed.2d 36 (1960). The Board of Education accelerated this voluntary transfer plan in 1965 so that it became effective with respect to two grades, rather than only one, each year, but dual schools continued under court order through the end of the 1966-67 school year. Ross v. Eckels, 11 Race Rep.L.Rep. 216 (S.D. Tex. 1965).

In July 1967, the district court granted the United States Government's motion to intervene as a plaintiff pursuant to Section 902 of the 1964 Civil Rights Act, 42 U.S.C. § 2000h-2. Two months later, in September 1967, the district court instituted a freedom of choice plan for school attendance pursuant to United States v. Jefferson County Bd. of Educ., 380 F.2d 385 (5th Cir.) (en banc), cert. denied, 389 U.S. 840, 88 S.Ct. 77, 19 L.Ed.2d 104 (1967). At the same time, the court ordered integration of transportation, physical facilities, athletics, and other extracurricular activities. Ross v. Eckels, 12 Race Rel.L.Rep. 2005 (S.D.Tex. 1967). HISD operated under this freedom of choice plan through the 1969-70 school year. Dissatisfied with the plan, the plaintiffs-appellants moved for supplemental relief in February 1968; the Government made a similar motion in February 1969. The district court held hearings on these motions in June 1969. On July 23, 1969, the court made an oral finding that the freedom of choice plan did not meet the requirements of Green v. New Kent County Bd. of Educ., 391 U.S. 430, 88 S.Ct. 1689, 20 L.Ed.2d 716 (1968) and Singleton v. Jackson Mun. School Dist., 419 F.2d 1211 (5th Cir. 1968) (per curiam), rev'd in part sub nom. Carter v. West Feliciana Parish School Bd., 396 U.S. 290, 90 S.Ct. 608, 24 L.Ed.2d 530 (1970), and directed HISD to devise a new desegregation plan.

In May 1970, after considering seven plans offered by the parties, the district court adopted an equidistant zoning plan for assignment of students that was scheduled to begin in September 1970. Zone lines were to be drawn equidistant between adjacent schools, with adjustments made to accommodate school capacities, city street patterns, and natural boundaries. Students were to attend schools in the zones where they resided at the time of enrollment regardless of change of residence during the year, unless they elected majority-to-minority transfers. On appeal, we prescribed several modifications in the plan. We ordered the district court to adopt a geographic capacity plan for the junior and senior high school levels, to pair twenty-four contiguous elementary schools and rezone another, and to assure transportation and priority for students electing majority-to-minority transfers. Ross v. Eckels, 317 F. Supp. 512 (S.D.Tex.), modified, 434 F.2d 1140 (5th Cir. 1970) (per curiam), cert. denied, 402 U.S. 953, 91 S.Ct. 1614, 29 L.Ed.2d 123 (1971). In September 1970, the district court amended its decree to implement the changes ordered by this court.

The elementary school pairing ordered in 1970 resulted largely in pairing and busing black and Hispanic students and in pairing schools attended by such students. This occurred for two reasons. While Hispanic students were classified as white for purposes of pairing schools, many non-Hispanic white families moved from the paired attendance areas or enrolled their children in private schools. White, black, and Hispanic parents all opposed transportation of their children from neighborhood to paired schools. The failure of pairing to achieve integration over a five-year period prompted HISD's General Superintendent, Billy Reagan, to recommend to the Board of Education (the Board) that a tri-ethnic community task force be appointed to consider an alternative to pairing. In November 1974, the Board authorized a Task Force for Quality Integrated Education. The task force was asked to develop an alternative to pairing that would promote integration, offer more educational opportunities, and stall or stop student flight by offering quality education. Through subcommittees, the task force conducted community hearings, reviewed the district's operations, visited other school districts, and consulted with, among others, representatives of the Justice Department. In its report to the Board of Education, the task force recommended a magnet school program.

Pursuant to this report, the Board appointed a tri-ethnic Administrative Task Team to develop a magnet school plan that would provide quality education, increase the percentage of students attending integrated schools, and decrease the number of one-race schools. In May 1975, HISD filed a motion to modify the desegregation plan by eliminating elementary school pairing and implementing this magnet school program. Neither the plaintiffs-appellants nor the Government opposed the plan, and it was approved by the district court on July 11, 1975. HISD implemented the plan in three phases over the 1975-76, 1976-77, and 1977-78 school years. Since its adoption, the number of magnet schools has increased from 41 to 62. In the 1978-79 school year, 7500 students attended magnet schools — 2600 whites, 3400 blacks, and 1500 Hispanics. Of that number, 3000 students were majority-to-minority transfers.

At the same time the district court approved the magnet school program, it also granted a motion by Hispanic plaintiffs to intervene in this action and, in 1977, it granted the Houston Teachers Association (HTA) leave to appear as amicus curiae.

As a further demonstration of its commitment to desegregation, HISD opposed an effort to disrupt its integration plans during the 1970's when private citizens attempted to form an independent school district that would be 89% white, 6% black, and 5% Hispanic. Operation of this proposed district, the Westheimer Independent School District (WISD), was aborted by our decision in Ross v. Houston Indep. School Dist., 559 F.2d 937, 939 (5th Cir. 1977) (per curiam) and subsequent district court action. See Ross v. Houston Indep. School Dist., 457 F. Supp. 18 (S.D.Tex. 1977), modified, 583 F.2d 712 (5th Cir. 1978).

In June 1978, the district court reviewed the history of desegregation in HISD and concluded that HISD "ha[d] no definite, high priority, well conceived plan to chart this district to the accomplishment of unitary status." The court ordered HISD to file a preliminary plan for reaching unitary status and directed it to address seven areas of concern to the court. In particular, HISD was asked to analyze the identifiably ethnic schools in the district to determine whether use of the tools described in Swann v. Charlotte-Mecklenburg Bd. of Educ., 402 U.S. 1, 91 S.Ct. 1267, 28 L.Ed.2d 554 (1971) could remove that identifiability; to consider possible interdistrict cooperation between HISD and predominantly white suburban school districts; and to address whether the magnet school program had been overemphasized. HISD filed its preliminary plan in August 1978. Ten months later, in June 1979, HISD, having concluded that its actions had achieved unitary status and that no further court-supervised action to that end was warranted, sought a declaration of unitary status and presented evidence in support of this contention. The Government requested a recess to prepare a full response, and in October responded to HISD's case. Significantly, the plaintiffs-appellants presented no evidence and no proposed findings.

In the interim, in September 1979, the court ordered the Texas Education Agency (TEA) to develop a plan based on voluntary cooperation and sharing of education opportunity to meet the challenges faced by HISD and other urban school districts. TEA filed a Voluntary Interdistrict Education Plan (VIEP) in March 1980 and HISD implemented it the following September. The plan is currently in operation in Houston and Harris County. HISD authorized tuition waivers and free transportation for VIEP participants, and has promoted VIEP in the surrounding school districts through the schools and the local media. HISD also created a Magnet School Task Force composed of community and educational leaders. The task force was instructed to oversee accommodation between VIEP and the magnet and vocational programs in the district.

In May 1980, the Government moved to amend its complaint and to add as defendants twenty-two surrounding school districts; the Harris County Department of Education and its Board of Trustees; the Texas Education Agency and the State Commissioners of Education; the City of Houston; and the State of Texas. The proposed amended complaint alleged that the "continuing racial segregation in the HISD system, and throughout the Houston metropolitan area, has been caused, in substantial part, by the intentional, racially discriminatory acts and omissions of both the HISD and the [added] defendants." The Government sought as relief the development of "a plan commensurate with the scope of the constitutional violations which will eliminate, to the maximum extent practicable, the remaining vestiges of the dual school system remaining in HISD and the Houston metropolitan area encompassed by HISD and the other defendant local school districts, without regard to school district boundaries and within a constitutionally acceptable period of time." In June 1980, the appellants filed similar motions which incorporated by reference the Government pleadings. The district court denied the Government's motion in a written memorandum and order on June 10, 1980. The next day the plaintiffs-appellants' motions were denied "for the same reasons."

Both the Government and the plaintiffs-appellants filed motions to alter or amend the district court's orders of June 10 and 11, 1980. These motions were denied in the court's memorandum and order of June 17, 1981. In that opinion, the district court also declared HISD to be a unitary school district.

The memorandum opinion of the district court offers five major reasons for refusing to broaden this litigation. First, the court noted that joinder of additional parties was not necessary for adjudication of the issue whether HISD had done everything practicable to remove vestiges of state-imposed segregation within its boundaries. Second, addition of twenty-six defendants "would inject as many more issues into an already complex case [and] similarly increase the discovery burdens upon all the litigants — both new and old. The ultimate resolution of HISD's unitary status would be postponed indefinitely, thus further extending what has already been an over-extended case." Third, the court noted that the question of an interdistrict solution had been brought to the attention of all parties in 1978 when the judge then presiding over this litigation ordered the Government to file a brief "collecting all recent authorities relating to inter-district relief." The Government brief was filed on August 9, 1978, in ample time to allow presentation of arguments and evidence on interdistrict relief at the 1979 hearings on HISD's attainment of unitary status. Denial of leave to amend was appropriate, because the Government and the appellants had known earlier the facts on which their proposed amendments were based, but had nonetheless omitted those facts from their earlier pleadings. Fourth, the defendants and all other interested parties would be prejudiced by further delay in reaching a decision on HISD's attainment of unitary status, as well as by the additional investigative and discovery expense occasioned by broadening the litigation. Finally, additional litigation would not guarantee any improvement in the court's ability to solve the problem of removing the vestiges of state-imposed segregation from HISD. The voluntary interdistrict plan already submitted by TEA, on the other hand, promised progress of the sort seemingly contemplated by the Government and the plaintiffs-appellants.

After considering all aspects of school district operations, the district judge also made the determination that HISD had achieved unitary status. The plaintiffs-appellants challenge only his finding that the district has eliminated the vestiges of de jure segregation in the composition of the student body of individual schools even though many schools are identifiably one-race. In determining whether the identifiable ethnicity of the district schools could be removed by further use of the tools discussed in Swann ( e.g., ethnic balancing, altering of attendance zones, elimination of one-race schools, pairing, and busing), the trial judge referred to the past experience and the current ethnic composition of the district. He concluded that "implementation of these techniques . . . would not be an effective and feasible remedy for this District; rather, it would be counterproductive to the HISD's desegregation efforts." Contrasting HISD with the Charlotte-Mecklenburg school district, the trial court asserted, "[t]he problems encountered in a rural, sparsely settled school district with only two schools and no concentrated residential segregation are quite different . . . ."

The court pointed out as reasons why further remedial efforts would be impracticable that HISD is the fifth largest school district in the nation and its student population and ethnic composition have both changed significantly after desegregation efforts began. The court accepted HISD's evidence that, to achieve greater integration without disrupting naturally integrated schools, it would be necessary to bus students to non-contiguous school zones. Based in part on housing-pattern maps filed in evidence, the district court found that, to accomplish racial integration by pairing schools, it would be necessary to pair schools on the extreme western and eastern ends of HISD. Otherwise, naturally integrated schools would be disturbed. The court considered several specific examples of the time and distance of representative runs throughout HISD. These representative studies show that the travel time between the west end of HISD and areas in the center and east end is considerable. There was also evidence that traffic in Houston is congested, requiring additional time for the completion of each existing bus route. The court "[did] not find it reasonable to subject children to compulsory cross-town bus rides of up to two hours one-way."

In addition, the court referred to the past inadequacies of busing as a desegregation tool in HISD. The court determined "HISD's remaining one-race schools are the product of its majority of black and Hispanic pupils rather than a vestige of past discrimination." There are not enough white students left in the district to effect greater integration of student bodies without untoward costs on the students themselves. The court retained jurisdiction over the case for three more years to insure that HISD maintained unitary status. HISD was ordered to file semi-annual reports on its operations. At the end of the three years, the court will conduct a hearing to determine whether this case should be dismissed.

During this litigation, every one of the original members of the HISD Board of Trustees and every member of several successive Boards has been replaced. Of the nine present members, five are white, three are black, and one is Hispanic. After the school district sought an end to court supervision, the plaintiffs-appellants followed the Government's lead by seeking leave to amend their complaint to add twenty-six defendants and to add a request for an inter-district remedy embracing schools in adjacent areas under the jurisdiction of other school boards. They appeal the district court's denial of this motion. They also contest the district court's determination that HISD has taken all practicable steps to eliminate the vestiges of state-imposed segregation and has achieved unitary status. They agree that all other indicia of segregation have been erased, but they assert that the unbalanced ethnic composition of the student populations in the schools is a residue not yet eliminated.

II.

A school system is not, of course, automatically desegregated when a constitutionally acceptable plan is adopted and implemented, for the remnants of discrimination are not readily eradicated. United States v. Texas Educ. Agency, 647 F.2d 504, 508 (5th Cir. 1981); Henry v. Clarksdale Mun. Separate School Dist., 579 F.2d 916, 921 (5th Cir. 1978) (per curiam) (Tjoflat, J., dissenting). Public school officials have a continuing duty to eliminate the systemwide effects of earlier discrimination and to create a unitary school system untainted by the past. Swann, 402 U.S. at 15, 91 S.Ct. at 1275, 28 L.Ed.2d at 566; see also Columbus Bd. of Educ. v. Penick, 443 U.S. 449, 459, 99 S.Ct. 2941, 2947, 61 L.Ed.2d 666, 677 (1979); Dayton Bd. of Educ. v. Brinkman, 443 U.S. 526, 538, 99 S.Ct. 2971, 2979-80, 61 L.Ed.2d 720, 734 (1979). They must demonstrate to the district court overseeing their desegregation efforts that "current segregation is in no way the result of [their] past segregative actions." Keyes v. School Dist. No. 1, 413 U.S. 189, 211 n. 17, 93 S.Ct. 2686, 2699 n. 17, 37 L.Ed.2d 548, 565 n. 17 (1973). The district court "should retain jurisdiction until it is clear that state-imposed segregation has been completely removed." Green v. New Kent County School Bd., 391 U.S. 430, 439, 88 S.Ct. 1689, 1695, 20 L.Ed.2d 716, 724 (1968); Raney v. Bd. of Educ., 391 U.S. 443, 449, 88 S.Ct. 1697, 1700, 20 L.Ed.2d 727, 732 (1968). State officials are responsible for state action, past as well as present. We have several times refused to find unitary a school system whose operation continues to reflect official failure to eradicate, root and branch, the weeds of discrimination. See United States v. Texas Educ. Agency, 647 F.2d 504 (5th Cir. 1981); Valley v. Rapides Parish School Bd., 646 F.2d 925, 926 (5th Cir. 1981); United States v. Bd. of Educ., 576 F.2d 37 (5th Cir.) (per curiam), cert. denied, 439 U.S. 1007, 99 S.Ct. 622, 58 L.Ed.2d 684 (1978); United States v. DeSoto Parish School Bd., 574 F.2d 804 (5th Cir. 1978); Mannings v. Board of Pub. Instruction, 427 F.2d 874 (5th Cir. 1970).

Communities in our mobile society do not, however, remain demographically stable. Swann, 402 U.S. at 31, 91 S.Ct. at 1283, 28 L.Ed.2d at 575. Therefore, "[n]either school authorities nor district courts are constitutionally required to make year-by-year adjustments of the racial composition of student bodies once the affirmative duty to desegregate has been accomplished and racial discrimination through official action is eliminated from the system." Id. at 32, 91 S.Ct. at 1284, 28 L.Ed.2d at 575. While those charged with desegregation must not shrink from the threat of white flight, school officials who have taken effective action have no affirmative fourteenth-amendment duty to respond to the private actions of those who vote with their feet. Pasadena City Bd. of Educ. v. Spangler, 427 U.S. 424, 434-36, 96 S.Ct. 2697, 2704, 49 L.Ed.2d 599, 607-08 (1976).

When state officials have not only made good-faith efforts to eliminate the vestiges of segregation, but have actually achieved a school system clean of every residue of past official discrimination, immutable geographic factors and post-desegregation demographic changes that prevent the homogenation of all student bodies do not bar judicial recognition that the school system is unitary. Calhoun v. Cook, 522 F.2d 717 (5th Cir.), reh'g denied, 525 F.2d 1203 (1975) (per curiam); Stout v. Jefferson County Bd. of Educ., 537 F.2d 800 (5th Cir. 1976).

III.

While we are free to re-assess the district court's conclusions of law, its findings of fact must be accepted unless they are clearly erroneous. Pullman-Standard v. Swint, 456 U.S. 273, 102 S.Ct. 1781, 72 L.Ed.2d 66 (1982). The plaintiffs-appellants question none of the court's findings concerning faculty assignment, transportation, extra-curricular activities, or facilities. They attack only the conclusion that HISD has done all that it practically can to eradicate the remnants of state-imposed segregation with regard to student assignment. First, they contend that inadequate desegregation efforts have been made because the district court has not required cross-district busing. Second, they decry the results achieved, since 70% of the black students in HISD still attend schools that are 90% or more minority, including as minorities black and Hispanic students.

The student population in twenty-two of the 226 schools in the system has been 90% or more black continuously since 1960. And there are now thirty-three more schools whose student population is 90% or more black. There are, however, only two all-white schools, both elementary. Fourteen of the twenty-two predominantly black schools were rezoned or paired in 1970 and were projected to be desegregated on a bi-racial basis. That goal failed when white students did not enroll in these public schools. Many of the remaining one-race black schools were at one time integrated or projected to be integrated, but all are now one-race because of housing patterns.

"We cannot properly review any student assignment plan that leaves many schools in a system one race without specific findings by the district court as to the feasibility of [using the] techniques [outlined in Swann]." Tasby v. Estes, 572 F.2d 1010, 1014 (5th Cir. 1978). See also Davis v. East Baton Rouge Parish School Bd., 570 F.2d 1260 (5th Cir. 1978). In making this determination adequate time-and-distance studies are desirable, if not indispensable. Tasby v. Estes, 572 F.2d at 1014. While the district court did not have time-and-distance studies for pairing all schools in the system, it did consider evidence of transportation problems that would be presented by pairing the only schools whose joinder could achieve significant reduction in predominantly one-race schools. As the district judge recognized, fear of white flight "cannot . . . be accepted as a reason for achieving anything less than complete uprooting of the dual public school system." United States v. Scotland Neck City Bd. of Educ., 407 U.S. 484, 491, 92 S.Ct. 2214, 2218, 33 L.Ed.2d 75, 81 (1972) (citation omitted). See also Monroe v. Bd. of Comm'rs, 391 U.S. 450, 459, 88 S.Ct. 1700, 1705, 20 L.Ed.2d 733, 739 (1968); Brown v. Bd. of Educ., 349 U.S. 294, 300, 75 S.Ct. 753, 756, 99 L.Ed. 1083, 1106 (1955) ( Brown II). However, in seeking reduction in the number of one-race schools, the district court could not ignore diminished white enrollment in HISD and substantial immigration of Hispanic students. Cf. Stout v. Jefferson County Bd. of Educ., 537 F.2d 800 (5th Cir. 1976). Even if some method were devised to spread white students equally among all schools in the system, 74% of the students in each school would be black and Hispanic.

The plaintiffs-appellants argue that the district court's order should be reversed because the court failed to require HISD to show that the large number of one-race schools remaining was not due to housing patterns that were the result of HISD's past segregative actions. The evidence showed that current housing patterns in Houston have evolved principally during the time that HISD has been under a desegregation order. They are, therefore, not the result of school board efforts to encourage or entrench segregation, but, insofar as they result from school attendance programs and not from other social and economic factors, a reaction to court-ordained policies. The school attendance impact, then, is the result of good-faith efforts to dismantle the dual school system, and not "the result of past segregative actions." Keyes v. School Dist. No. 1, 413 U.S. at 211 n. 17, 93 S.Ct. at 2699 n. 17, 37 L.Ed.2d at 565 n. 17. Current housing patterns may still show the lingering effects of school board actions that preceded the 1970 desegregation order, but we are not persuaded that the district judge was in error when he rejected the possible probative value of further proceedings to demonstrate that earlier housing patterns resulted from official school segregation policy apart from other community economic and social influence. We do not reject the district court's finding that HISD has done everything practicable at an intradistrict level to eradicate the effects of past segregative practices. After twelve years of court-supervised desegregation efforts, this case has reached the stage where no benefit can be derived from further probing for the perhaps unmeasurable sins of the past because no additional remedies are available from the efforts of HISD alone. (We consider below the effort to join other parties.)

The district judge did not turn his back on this case. He followed the procedure we have required to assure that a determination of unitary status is not prematurely reached. United States v. State of Texas, 509 F.2d 192 (5th Cir. 1975); Youngblood v. Bd. of Pub. School Instruction, 448 F.2d 770 (5th Cir. 1971) (per curiam). He has retained jurisdiction over the action for three more years. During that time, the school district must file semi-annual operational reports. At the end of three years, he will hold a hearing at which the plaintiffs may show why dismissal of the action should be delayed. Following the hearing, he will finally determine whether the school district has indeed achieved unitary status. Only then, if appropriate, may he dismiss the action.

The plaintiffs-appellants have not come forward with an alternative desegregation plan. In the twelve years that HISD has operated under a court-ordered desegregation plan, they have made no request for additional relief, yet today they are the sole appellants from the district court's order. Neither the Government, the Hispanic plaintiff group, nor the HTA, as amicus curiae, joins in this appeal. For over a decade the plaintiffs-appellants have followed the lead of other parties who are apparently now satisfied with the result. In the adversary system mandated by the Constitution, Art. III, § 1, it is the duty of the parties to assert their position, to adduce evidence, and, in institutional litigation, to suggest remedial measures. It does not suffice under the circumstances for the lone dissenter from the court's order simply to assert that more evidence must be studied and more plans must be considered. That evidence must be brought before the court; those plans must be presented to the court.

In testing whether the past has been eradicated so far as it remains in the power of school officials and courts to do so, we must keep in mind that each school district is unique. The constitutional mandate against racial discrimination is categoric, but the determination of remedies for its past violation turns on the conditions in a particular district. Ross v. Eckels, 434 F.2d 1140, 1147 (5th Cir. 1970) (per curiam), cert. denied, 402 U.S. 953, 91 S.Ct. 1614, 29 L.Ed.2d 123 (1971). In like fashion, the decision that public officials have satisfied their responsibility to eradicate segregation and its vestiges must be based on conditions in the district, the accomplishments to date, and the feasibility of further measures. HISD has not adopted, and the district court has not required it to utilize, all of the remedial measures mentioned in Swann. Those techniques are not mandatory; they are merely permissible. HISD has used many of them — for example, rezoning, pairing and clustering. Other techniques, such as non-contiguous pairing and further mandatory transfers, have been considered by HISD and the district court on several occasions, but have been rejected as unsuitable. Constructing a unitary school system does not require a racial balance in all of the schools. Swann, 402 U.S. at 24, 91 S.Ct. at 1280, 28 L.Ed.2d at 571; Horton v. Lawrence County Bd. of Educ., 578 F.2d 147, 151 (5th Cir. 1978) (per curiam); United States v. Bd. of Educ., 576 F.2d at 39. What is required is that every reasonable effort be made to eradicate segregation and its insidious residue.

Considering 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, we conclude that the district court made no error in declaring the system unitary while retaining supervision of it for three more years. We resolutely affirm the commitment of this circuit to requiring school officials faithfully to execute the commandment of the fourteenth amendment in concluding that HISD is a singular district, with unusual, perhaps unique, problems and that, therefore, the district court did not err.

IV.

The district court refused to permit an amendment to the pleadings to assert a claim that interdistrict relief embracing student transfers throughout the Houston metropolitan area may be appropriate. Although the plaintiffs-appellants appealed this ruling, at oral argument they conceded that it would not prejudice them as long as they were permitted to file a separate suit for an interdistrict remedy. They characterized the denial of leave to amend as a secondary matter. Their only concern was that the new suit be heard by the judge presiding over this litigation, because of his familiarity with the facts and issues.

Once a responsive pleading has been filed, a pleading may be amended only by leave of court or by consent of the adverse party. Fed.R.Civ.P. 15(a). While "leave shall be freely given when justice so requires," the decision rests in the sound discretion of the trial court. Zenith Radio Corp. v. Hazeltine Research, Inc., 401 U.S. 321, 330, 91 S.Ct. 795, 802, 28 L.Ed.2d 77 (1971); Foman v. Davis, 371 U.S. 178, 182, 83 S.Ct. 227, 230, 9 L.Ed.2d 222, 226 (1962). When the motion is presented after undue delay or when it would occasion undue prejudice to the opposing party, the denial of leave is a proper exercise of the district court's discretion. Foman v. Davis, 371 U.S. at 182, 83 S.Ct. at 230, 9 L.Ed.2d at 226; 3 J. Moore, Federal Practice § 15.08[4] (2d ed. 1982); 6 C. Wright A. Miller, Federal Practice and Procedure: Civil §§ 1487, 1488 (1971). Our review extends only to whether the trial court abused that discretion. Carson v. Polley, 689 F.2d 562, 583 (5th Cir. 1982); Harkless v. Sweeny Indep. School Dist., 554 F.2d 1353, 1359 (5th Cir. 1977).

The district court here denied relief because the proposal to amend came so late in the proceeding that its allowance would prejudice HISD. As we have noted, the motion to amend was first presented in 1980 after the hearing on unitary status had been held and twenty-four years after the complaint was filed. While the proposed amended complaint asserts that the putative defendants "have been engaged" in unconstitutional actions "for a substantial period of time" "during the time of statutory dual school systems and thereafter," the complaint does not particularize when the actions occurred. The briefs refer to actions taken both before and after Brown I, with emphasis on events in the 1950's and 1960's. There is no suggestion that any such efforts have occurred recently.

The plaintiffs-appellants justify their failure to raise the claim for interdistrict relief earlier on the ground that the possibility of interdistrict relief first came to their attention when the district court issued its 1978 order to HISD. But the question of HISD's relationship to surrounding school districts surfaced implicitly as early as 1970 in our discussion of HISD's location with respect to adjacent school districts and governmental subdivisions. Ross v. Eckels, 434 F.2d at 1141-42 n. 2. We disclaimed any intention of raising questions at that time about the "constitutional dimensions of problems presented by racial distinctions resulting from the shape and relationship of artificial geographic boundaries of counties, municipalities and school districts." Id. at n. 2 (citation omitted). See also id. at 1150 (Clark, J., dissenting); Ross v. Houston Indep. School Dist., 457 F. Supp. 18, 25 (S.D. Tex. 1977). This certainly directed attention to the issue, and left the way clear for the plaintiffs-appellants to assert their claim.

In June 1977, counsel for the plaintiffs-appellants was informed of transfers of black students from Spring Branch Independent School District to other school districts. In 1978, the district court ordered a submission by the Department of Justice concerning the court's legal authority to order interdistrict relief. In April 1978, an attorney for the HTA argued to the district court that there was a need for a metropolitan desegregation plan. Because they had all of this information, the plaintiffs-appellants cannot reasonably claim that they did not know any of the facts that formed the basis for their motion. While the Government also sought to inject this issue into the proceedings in 1980, it does not appeal the district court's denial of its motion.

We find no abuse of discretion in the district court's denial. The motion was not only belated. Amendment of the pleadings would add new and complex issues to a case already protracted and complicated. It would require new discovery, additional hearings, and, likely, more appeals. It would add twenty-six new parties, including a number of separate school districts. The preparation and trial of the case, by the plaintiffs-appellants' own estimate, would require several years. The allowance of the amendment would undoubtedly prejudice HISD. See Troxel Mfg. Co. v. Schwinn Bicycle Co., 489 F.2d 968, 971 (6th Cir. 1973), cert. denied, 416 U.S. 939, 94 S.Ct. 1942, 40 L.Ed.2d 290 (1974).

The plaintiffs-appellants protest that the motion was denied without a hearing. The Local Rules of the Southern District of Texas provide that a hearing will be held on such a motion only if one is requested by other parties or ordered by the court. The plaintiffs-appellants made no such request, nor did any other party. Indeed, the only factual evidence suggested to the district court or to us on appeal that might have affected the decision is the affidavit of plaintiffs' counsel, Weldon H. Berry, that he personally did not learn earlier of the existence, pattern, and extent of the inter-district constitutional violations committed by HISD and the parties sought to be joined. As our review of the record shows, there was, long before, ample reason for the plaintiffs-appellants and their then counsel to be aware of facts that suggested the issue now sought to be raised.

Moreover, the district court's denial of leave to amend because of the plaintiffs-appellants' undue delay is not the equivalent of a judgment on the merits. The basis for relief presented in the proposed amendment differs from the basis set forth in the original complaint filed twenty-four years earlier. Some of the acts complained of apparently occurred after this suit was filed and could not, therefore, have been asserted when the complaint was drafted.

While we have noted events between 1970 and 1978 that should have alerted the plaintiffs-appellants to the possible claim for interdistrict relief, the delay that bars assertion of the claim in this action is not the same as laches or abandonment that would cause the claim to be irretrievably lost. While the district court's order denying leave to amend does not expressly preserve the plaintiffs-appellants' right to file a new suit raising the issues asserted in the proposed amendment, such a reservation is implicit in its decision, and we now make it explicit, for, were the denial of leave equivalent to a determination on the merits, we would consider it an abuse of discretion. The door is thus left open to new litigation, and we do not foreclose either its institution or the presentation of any defenses that might be asserted, such as laches. Neither do we foreclose, indeed we commend, the assignment of any new litigation to the judge who is familiar with the HISD litigation.

Because we agree that the motion to amend the complaint was properly denied, we need not discuss the permissibility of joinder of new parties. We note, however, that the plaintiffs-appellants urge that joinder of the additional parties is necessary because in their absence complete relief cannot be accorded among those already parties. Fed.R.Civ.P. 19(a). If the issue of interdistrict collaboration in unconstitutional actions were before the court, this contention would have merit. But, in the absence of that issue, those parties are not necessary to, or affected by, the order appealed from. That order determines only that HISD has done all it can within its borders to purge itself of the vestiges of intradistrict segregation. Rule 19 can be utilized only to bring in parties necessary to a complete and just adjudication of the issues presently before the court. La Chemise La Coste v. General Mills, Inc., 53 F.R.D. 596, 601 (D.Del. 1971), aff'd, 487 F.2d 312 (3d Cir. 1973).

V.

During the past twelve years of court-supervised desegregation, HISD and the successive trial judges who have presided over this litigation have made sustained good-faith efforts to create a unitary school system. The unique difficulties of a large urban school district with a rapidly expanding minority population, surrounded by a constellation of racially stratified suburban school districts, have forestalled student integration within HISD's boundaries although all other aspects of school operation are free of past racist taint. The district court did not err in the factual findings on which it based its decision that HISD has successfully erased the internal vestiges of state-imposed educational segregation. The district court continues to monitor HISD to insure that its finding of unitary status continues to be warranted. In the future, it will conduct a hearing on the question whether it should relinquish jurisdiction, over this case. If there are then reasons for it to continue to exercise jurisdiction, that evidence should be presented to it. In the meantime, the plaintiffs-appellants are free to seek interdistrict relief through a new suit addressing the alleged discriminatory actions HISD undertook in conjunction with officials of the state of Texas, the city of Houston, Harris County, and neighboring school districts. Compare Stevenson v. International Paper Co., 516 F.2d 103, 110-11 (5th Cir. 1975) (suit challenging joint union-company policies not precluded by suit challenging union action).

For these reasons, the judgment is AFFIRMED, and the case is REMANDED to the district court for further proceedings in accordance with this opinion.