We have consolidated for argument and decision nine separate appeals, plus one petition for mandamus, arising out of the remedial phase of the Rockford, Illinois desegregation litigation. The current lawsuit is "only" eight years old, but litigation over racial segregation in the Rockford public schools began a quarter of a century ago, see Quality Education for All Children, Inc. v. School Board, 362 F.Supp. 985 (N.D.Ill.1973), and we have heard many appeals in it. The recent flurry of appeals, threatening to become an avalanche, induced us to direct that all pending and future appeals be submitted to this panel.

We need go no farther back in the history of this litigation than 1994, when the district judge found that the school district had intentionally discriminated against black and Hispanic students in violation of the equal protection clause of the Fourteenth Amendment. 851 F.Supp. 905 (N.D.Ill.1994). That discrimination was not, of course, commanded or authorized by state or local law, like the school segregation invalidated in Brown v. Board of Education, 347 U.S. 483, 74 S.Ct. 686, 98 L.Ed. 873 (1954); see also Brown v. Board of Education, 892 F.2d 851, 854 (10th Cir.1989), vacated, 503 U.S. 978, 112 S.Ct. 1657, 118 L.Ed.2d 381 (1992); on remand, 978 F.2d 585 (10th Cir.1992). The inference of intentional discrimination was drawn primarily from disparities in educational achievement between white and minority students and from the school district's failure to take effective steps to prevent its schools from becoming all-white or all-minority. The school district accepted the determination of liability, and the parties consented to have a magistrate judge preside over the remedial phase of the litigation with power to enter judgment pursuant to 28 U.S.C. § 636(c).

The magistrate judge appointed a special master to assist him, pursuant to Fed.R.Civ.P. 53, and in 1996, after evidentiary hearings, entered an elaborate equitable decree (the "comprehensive remedial order"). The decree contains a number of provisions concerning the operation of the school district that are assailed in the appeals by the school district and the teachers' and other school employees' unions. The appeal of the plaintiffs, who brought this suit on behalf of minority children in the school district, focuses on the omission from the decree of provisions proposed by either the plaintiffs or the special master. A number of the provisions in the decree are not challenged by any party, including ones designed to give parents a measure of choice about which school within the school district to send their children to and, most important, ones requiring racial integration of each school in the district. The decree also requires the school district to build additional schools at an estimated cost of $48 million. That provision is not challenged either, but the school district does challenge the method that the magistrate judge decreed, in separate orders, for financing the building program. A third set of challenges by the school district is to two orders by the magistrate judge regarding the special master's role in a hearing on the implementation of one of the remedial measures.

The discretionary power of a district court to formulate an equitable remedy for an adjudicated violation of law is broad. Where necessary for the elimination of the violation, the decree can properly fence the defendant in by forbidding conduct not unlawful in itself. FTC v. National Lead Co., 352 U.S. 419, 430, 77 S.Ct. 502, 509, 1 L.Ed.2d 438 (1957); Sasnett v. Sullivan, 91 F.3d 1018, 1021 (7th Cir.1996); Szabo v. U.S. Marine Corp., 819 F.2d 714, 721 (7th Cir.1987). But equitable discretion is not unlimited, and a number of principles have emerged to guide its exercise. For example, because the violation of an equitable decree is punishable as a contempt of court, the decree should not command the defendants to do something that is entirely beyond their control. Haley v. Pataki, 883 F.Supp. 816, 826 (N.D.N.Y.), vacated as moot, 60 F.3d 137 (2d Cir. 1995); Cook v. Rockwell Int'l Corp., 755 F.Supp. 1468, 1483 (D.Colo.1991); cf. Pasadena City Board of Education v. Spangler, 427 U.S. 424, 438-40, 96 S.Ct. 2697, 2705-07, 49 L.Ed.2d 599 (1976). Moreover, equitable decrees often affect innocent third parties; their interests must be fully considered in the formulation of the decree, especially when the interests are of constitutional dignity. People Who Care v. Rockford Board of Education, 961 F.2d 1335, 1338 (7th Cir.1992); Walgreen Co. v. Sara Creek Property Co., 966 F.2d 273, 276 (7th Cir.1992); NLRB v. P*I*E Nationwide, Inc., 894 F.2d 887, 893 (7th Cir.1990); Duran v. Elrod, 760 F.2d 756, 759 (7th Cir.1985); cf. Madsen v. Women's Health Center, Inc., 512 U.S. 753, 765-66, 114 S.Ct. 2516, 2524-25, 129 L.Ed.2d 593 (1994). And when the decree is addressed to a branch of government rather than to private persons, it must be formulated with sensitivity to the separation of powers and the dignity of the states as quasi-sovereigns. Rizzo v. Goode, 423 U.S. 362, 378-79, 96 S.Ct. 598, 607-08, 46 L.Ed.2d 561 (1976); Association of Community Organizations for Reform Now (ACORN) v. Edgar, 56 F.3d 791, 798 (7th Cir.1995); Hoover v. Wagner, 47 F.3d 845, 850-51 (7th Cir.1995). Some of these interbranch decrees are ambitiously designed to reform important public institutions. In such cases the court must be sensitive not only to the concerns of comity but also to the practical limitations of the federal judiciary as an administrative body, in this case a super school board. Turner v. Safley, 482 U.S. 78, 84-85, 107 S.Ct. 2254, 2259-60, 96 L.Ed.2d 64 (1987); Bell v. Wolfish, 441 U.S. 520, 547-48, 99 S.Ct. 1861, 1878-79, 60 L.Ed.2d 447 (1979); Stone v. City & County of San Francisco, 968 F.2d 850, 860-61 (9th Cir.1992).

The court must also bear in mind the general precept, which is the valid core of equity's former reluctance to decree mandatory relief, 1 Dan R. Dobbs, Law of Remedies: Damages--Equity--Restitution § 2.9, pp. 224-25 (2d ed.1993), that decrees which prohibit specified conduct are generally preferable to those that impose affirmative duties. They are easier to obey and easier to enforce than decrees that command the defendant to do something rather than to desist from doing something, and by so commanding enmesh the federal courts in administration. Affirmative decrees are a formula for protraction. Forty-eight years after it had first been initiated, litigation to desegregate the public schools of Topeka was still producing appeals generating 100-page judicial opinions. Brown v. Board of Education, supra, 892 F.2d at 851-957.

It should go without saying that equitable remediation must be guided by norms of proportionality. Dalton v. Little Rock Family Planning Services, 516 U.S. 474, ---- - ----, 116 S.Ct. 1063, 1064-65, 134 L.Ed.2d 115 (1996) (per curiam); Dayton Board of Education v. Brinkman, 433 U.S. 406, 417, 419, 97 S.Ct. 2766, 2774, 2775, 53 L.Ed.2d 851 (1977); Swann v. Charlotte-Mecklenburg Board of Education, 402 U.S. 1, 22, 91 S.Ct. 1267, 1279, 28 L.Ed.2d 554 (1971); Waldman Publishing Corp. v. Landoll, Inc., 43 F.3d 775, 785 (2d Cir.1994); Gulf Oil Corp. v. Brock, 778 F.2d 834, 842-43 (D.C.Cir.1985); Ameron, Inc. v. U.S. Army Corps of Engineers, 787 F.2d 875, 888, 890 (3d Cir.1986). That is, the remedy must be tailored to the violation, rather than the violation's being a pretext for the remedy. Violations of law must be dealt with firmly, but not used to launch the federal courts on ambitious schemes of social engineering. Cf. Swann v. Charlotte-Mecklenburg Board of Education, supra, 402 U.S. at 22, 91 S.Ct. at 1279. Children, the most innocent of the innocent persons occasionally brushed by draconian decrees, should not be made subjects of utopian projects.

A related point, as we shall see, is that the guidelines for the admissibility of expert testimony that the Supreme Court laid down in Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579, 113 S.Ct. 2786, 125 L.Ed.2d 469 (1993), apply to the testimony of social scientists as well as to that of natural scientists. Sheehan v. Daily Racing Form, Inc., 104 F.3d 940, 942 (7th Cir.1997); Tyus v. Urban Search Management, 102 F.3d 256, 263 (7th Cir.1996). And not only to their testimony at the liability stage of a lawsuit, but also to testimony offered at the remedy stage.

Every one of these precepts was violated by one or more provisions of the decree in this case. Consider first the provision that at least 13.5 percent of the teachers in each school in the school district be black or Hispanic and that they be given superseniority so that in the event of layoffs the percentage of minority teachers will not dip below the prescribed level. No teachers are even plaintiffs in this suit. And while there are references in the district judge's opinion on liability to the underrepresentation of minority teachers (currently 8.7 percent) in the school district's teaching staff, there is no finding that the school district has ever discriminated (by which we mean discriminated intentionally--the only kind of discrimination that violates the equal protection clause, Dayton Board of Education v. Brinkman, supra, 433 U.S. at 413, 97 S.Ct. at 2772; Washington v. Davis, 426 U.S. 229, 96 S.Ct. 2040, 48 L.Ed.2d 597 (1976); Barnett v. Daley, 32 F.3d 1196, 1198-99 (7th Cir.1994)) in the hiring, promotion, firing, assignment (to one school or another), or transfer of teachers. See 851 F.Supp. at 923-24. The magistrate judge thought he was finding intentional discrimination in hiring, see id. at 1130, but he based his finding of intentional discrimination on statistical disparities, which need not reflect discrimination, intentional or otherwise, and on the school district's failure to reach its self-imposed hiring goals--so that failure to achieve affirmative action was treated, erroneously, Yatvin v. Madison Metropolitan School District, 840 F.2d 412, 415-16 (7th Cir.1988); Mozee v. American Commercial Marine Service Co., 940 F.2d 1036, 1051 (7th Cir.1991), as a form of intentional discrimination against the beneficiaries of the affirmative action. The record does not support an inference of intentional discrimination against black or Hispanic teachers. The white teachers currently employed by the school district who will lose seniority rights, and future white applicants for teaching jobs who will be discriminated against in favor of minority applicants, cannot be deemed to owe their jobs, their job prospects, or their seniority to being beneficiaries of past discrimination against minorities.

These white teachers are to be made victims of court-decreed racial discrimination in order to secure to the minority students the conjectural benefits of making it more difficult to identify particular schools as "white" or "black" (or Hispanic), of reducing the disciplinary problems of minority students--problems assumed to be less serious if their teachers are black or Hispanic--and of fostering achievement by providing minority students with role models of their own race or ethnicity. Although such benefits may be real, the evidence for them in the record of this case is scanty. More important, it is not the kind of evidence that justifies infringing the constitutional right not to be discriminated against in hiring and seniority on account of race. Wygant v. Jackson Board of Education, 476 U.S. 267, 274-76, 106 S.Ct. 1842, 1847-48, 90 L.Ed.2d 260 (1986) (plurality opinion); id. at 294-95, 106 S.Ct. at 1857-58 (separate opinion).

It is true that "reverse discrimination"--discrimination by whites against whites because of race--is not unlawful per se, at least when it is intended to remedy past misconduct by the reverse discriminator, Adarand Constructors, Inc. v. Pena, 515 U.S. 200, ----, 115 S.Ct. 2097, 2117, 132 L.Ed.2d 158 (1995) (plurality opinion), and perhaps in a few other types of case as well. Wittmer v. Peters, 87 F.3d 916 (7th Cir.1996). But it is highly suspect, e.g., Shaw v. Reno, 509 U.S. 630, 642-43, 113 S.Ct. 2816, 2824-25, 125 L.Ed.2d 511 (1993), and therefore, as we emphasized in Wittmer, has to be justified by solid evidence. This is especially true when it takes the form of a quota embodied in an equitable decree and hence enforceable by contempt sanctions and continuing federal judicial control. See Lockett v. Board of Education, 92 F.3d 1092, 1101 (11th Cir.1996); Tasby v. Estes, 643 F.2d 1103, 1105 (5th Cir.1981). The threat of sanctions and protracted federal tutelage would place pressure on the school district to relax its hiring standards as much as was necessary to fill the quota, with the almost certain consequence that the teachers it was hiring would on average not be as good as if it were on the basis purely of merit. To make a case for reverse discrimination the reduction in quality would at a minimum have to be traded off against the benefits in racial and ethnic matching, and this has not been done. The incremental benefits--not the benefits of having a substantial percentage of minority teachers but the benefits of having 13.5 percent rather than the current 8.7 percent--would have to be compared with the costs in reduced quality of teachers, and that comparison has not been made either. And because the percentage of minority teachers currently being hired by the school district is well above 13.5 percent, the district is on its way toward that level anyway, cf. Dayton Board of Education v. Brinkman, supra, 433 U.S. at 411, 97 S.Ct. at 2770, so that the quota probably is unnecessary as well as--on this record, which does not begin to justify a racial quota for teachers--unconstitutional. Britton v. South Bend Community School Corp., 819 F.2d 766, 771-72 (7th Cir.1987) (en banc).

What makes this aspect of the comprehensive remedial order even more troubling is that it contravenes the statement by this court in an earlier opinion in this lawsuit that "changing seniority or other contractual rights would make the remedial job easier, but this does not license a court to impose these changes on persons who have done no wrong." People Who Care v. Rockford Board of Education, supra, 961 F.2d at 1338. That is what the magistrate judge has done, in violation of the law of the case doctrine--as well as of the Constitution.

Several of the challenged provisions of the decree relate to class assignment of students. The decree forbids tracking--that is, grouping students by ability. There are some exceptions; for example, classes for especially gifted students are permitted. But the exceptions are illusory, because even in those classes the decree imposes racial quotas. And, what is closely related to the prohibition of tracking, the decree requires that the racial composition of every nonelective class in every school in the district match the racial composition of the school, with a leeway of only 5 percent. So in a class of 30 students in a school in which 40 percent of the students are minority students, there must be between 35 percent and 45 percent minority students--which is to say no fewer than 10 minority students nor more than 14--or else the decree is violated. That is a misplaced exactitude.

Tracking is a controversial educational policy, although just grouping students by age, something no one questions, is a form of "tracking." Lawyers and judges are not competent to resolve the controversy. The conceit that they are belongs to a myth of the legal profession's omnicompetence that was exploded long ago. To abolish tracking is to say to bright kids, whether white or black, that they have to go at a slower pace than they're capable of; it is to say to the parents of the brighter kids that their children don't really belong in the public school system; and it is to say to the slower kids, of whatever race, that they may have difficulty keeping up, because the brighter kids may force the pace of the class. "The vast majority of public school students in the United States are tested, ranked, and segregated into separate ability groups and classes based on standardized test performance." Note, "Teaching Inequality: The Problem of Public School Tracking," 102 Harv. L.Rev. 1318 (1989) (footnote omitted). This may be deplorable, as the author of the student note (who at the time of writing the note was neither a public school student nor, it is a safe guess, a parent) believes, id. at 1340-41; but as the consensus of the nation's educational authorities, it deserves some consideration by a federal court.

Were abolition of tracking the only means of preventing the school district from manipulating the tracking system to separate the races, it might be a permissible remedy. It is not the only way--as we take the plaintiffs implicitly to concede by accusing the school district of having placed white kids in higher tracks, and black kids in lower tracks, without always complying rigorously with objective criteria, such as scores on achievement tests. If that is the wrong, the remedy is obvious: forbid the district, on pain of contempt if the prohibition is flouted, to track students other than in accordance with criteria that have been validated as objective and nonracist. Quarles v. Oxford Municipal Separate School District, 868 F.2d 750, 754-55 (5th Cir.1989). This form of remedy is not only proportioned to the violation and duly respectful of the autonomy of educators in matters educational; it also requires less administrative supervision by the special master (and hence by the magistrate judge), who under the existing decree must supervise the school district's decisions on what courses to make elective and must police the absurdly confining 5 percent tolerances.

Tracking might be adopted in order to segregate the races. The well-known correlation between race and academic performance makes tracking, even when implemented in accordance with strictly objective criteria, a pretty effective segregator. If tracking were adopted for this purpose, then enjoining tracking would be a proper as well as the natural remedy for this form of intentional discrimination, at least if there were no compelling evidence that it improves the academic performance of minority children and if the possible benefits to the better students and the social interest in retaining them in the public schools were given little weight. The general view is that tracking does not benefit minority students, Daniel U. Levine & Rayna F. Levine, Society and Education 38-41 (9th ed.1996), although there is evidence that some of them do benefit. Adam Gamoran & Robert D. Mare, "Secondary School Tracking and Educational Inequality: Compensation, Reinforcement, or Neutrality?" 94 Am. J. Sociology 1146, 1177 (1989). All this is neither here nor there. The plaintiffs' argument is not that the school district adopted tracking way back when in order to segregate the schools. It is that it misused tracking, twisting the criteria to achieve greater segregation than objective tracking alone would have done. See 851 F.Supp. at 913-14. The school district should be enjoined from doing this--not, on this record, enjoined from tracking.

To the extent that tracking is restored, classroom racial quotas will go by the board; they are incompatible with tracking. In classes that are not tracked, the magistrate judge will have to reexamine the use of such quotas; the 5 percent tolerances are too tight.

Another unjustifiable provision of the decree is the requirement that within four years half the gap in test scores between the white and minority students be closed. The main objections are not to the period of years, absurdly short though it seems, but to requiring the school district, under pain of contempt sanctions if it fails, to achieve a goal that depends to a significant degree on circumstances beyond its control--were there a feasible means, decreeable by a court, of closing the gap in educational achievement between white and black students, the gap would have been closed by now--and to ascribing half the gap to past discrimination by the school district. The 50 percent estimate is the magistrate judge's, and though it is purportedly based on testimony by expert witnesses about the achievement gap, no witness attempted to measure the size of the gap attributable to discrimination by the school district. One did say that 30 percent of the gap was attributable to poverty. But this made it merely possible, not probable--in fact highly improbable, as we are about to see--that the rest of the gap was due to discrimination (intentional discrimination, that is) by the school district.

The only study of the achievement gap that was conducted for this lawsuit did not attempt to quantify the causes of the gap and was in any event inadmissible under the Daubert test. That test requires, so far as bears on this case, that the methods used by the expert to derive his opinion satisfy the standards for scientific methodology that his profession would require of his out-of-court research. Sheehan v. Daily Racing Form, Inc., supra, 104 F.3d at 942; Braun v. Lorillard Inc., 84 F.3d 230, 235 (7th Cir.1996); Raynor v. Merrell Pharmaceuticals Inc., 104 F.3d 1371, 1375 (D.C.Cir.1997). The test is not whether his results are accepted by his scientific peers, but whether the methods he used to obtain them are good science or pseudoscience. The study in question, designed to correct for the influence of poverty on academic test scores, compared the scores of the poor white students in the school district with those of the poor minority students, with "poor" defined solely as receiving free lunches. The implicit assumption was thus that the only factor other than discrimination by the school district that could cause minority students to underperform white students on scholastic tests is poverty. The study did not even measure poverty. It merely identified students who were below a poverty line. Even if the line was correctly chosen, the black students eligible for free lunches could be on average significantly poorer than the white students eligible for them; they could be further below the poverty line, and this could make a difference in their educational achievement. And poverty is not the only family or demographic characteristic affecting scholastic performance. If it were, the well-documented scholastic achievements of the children of poor immigrants would have to be ascribed to discrimination in favor of immigrants! The social scientific literature on educational achievement identifies a number of other variables besides poverty and discrimination that explain differences in scholastic achievement, such as the educational attainments of the student's parents and the extent of their involvement in their children's schooling. E.g., David J. Armor, Forced Justice: School Desegregation and the Law 96, 98 (1995); James S. Coleman, Equality of Educational Opportunity 302 (1966). These variables cannot be assumed to be either randomly distributed across the different racial and ethnic groups in Rockford or perfectly correlated with poverty. There isn't even evidence that the gap in scholastic achievement between white and minority students in Rockford is any greater than the gap between white and minority students in school districts that have not been found to have discriminated against their black and Hispanic students.

A statistical study is not inadmissible merely because it is unable to exclude all possible causal factors other than the one of interest. But a statistical study that fails to correct for salient explanatory variables, or even to make the most elementary comparisons, has no value as causal explanation and is therefore inadmissible in a federal court. The idea that the educational deficiencies of minority students in the Rockford public schools are due primarily to discrimination by the school authorities and can be rectified by an equitable decree is at once unsubstantiated by responsible evidence and--since there is no evidence that these deficiencies are any greater than in school districts around the country that have not been held to have discriminated against minority students--implausible.

The decree forbids the school district to refer a higher percentage of minority students than of white students for discipline unless the district purges all "subjective" criteria from its disciplinary code. The decree requires this even though important disciplinary criteria (such as disrupting classes) are unavoidably judgmental and hence "subjective" within the sense of the decree, and even though the disparity in minority and white referrals is smaller in the Rockford school district than in the nation as a whole. This provision cannot stand. Coalition to Save Our Children v. State Board of Education, 90 F.3d 752, 775 (3d Cir.1996); Keyes v. Congress of Hispanic Educators, 902 F.Supp. 1274, 1303-04 (D.Colo.1995). Racial disciplinary quotas violate equity in its root sense. They entail either systematically overpunishing the innocent or systematically underpunishing the guilty. They place race at war with justice. They teach schoolchildren an unedifying lesson of racial entitlements. And they incidentally are inconsistent with another provision of the decree, which requires that discipline be administered without regard to race or ethnicity.

The decree also perversely limits minority enrollment in compensatory education (that is, remedial) programs to the percentage of minority students in the school as a whole. These programs are designed largely although not entirely for minority students, because they have on average more educational deficits. To forbid these students access to these programs on the ground that it would foster unfavorable stereotypes is the kind of "benign discrimination" thinking (illustrated by Bradwell v. Illinois, 83 U.S. (16 Wall.) 130, 141-42, 21 L.Ed. 442 (1873) (concurring opinion)) that the courts have long rejected. See, for recent examples, United States v. Starrett City Associates, 840 F.2d 1096, 1102 (2d Cir.1988); Larkin v. Michigan, 883 F.Supp. 172, 176-77 (E.D.Mich.1994). It is impermissible.

No party defends the provision of the decree that limits the amount of money that the school district may take from "Fund 12" to finance compliance with the decree. Fund 12 is part of a tort immunity fund, which is a fund that local government agencies in Illinois are authorized by state law to create out of revenue from property taxes in order to pay tort judgments. 105 ILCS 5/17-2.5; 745 ILCS 10/9-107. The question whether it is lawful under Illinois law to use the tort fund for compliance with a desegregation decree is currently before the Illinois courts. We cannot fathom the magistrate judge's desire to "wean" the school district from its dependence on this fund to finance compliance with the decree, especially given the limits that Illinois law places on the power of local government to raise property taxes. 35 ILCS 200/18-185 to -245; 105 ILCS 5/12-11.1, 5/17-2.

Another indefensible provision of the decree prescribes the racial and ethnic composition of the cheerleading squads. The percentage of cheerleaders in each school who are black or Hispanic must be no lower than the corresponding percentage of the school's population as a whole. Of course the school district may not discriminate against minority aspirants for the cheerleading squads. But to fix a racial quota for cheerleaders demeans the remedial process in school desegregation litigation and cannot possibly be justified in the absence of evidence (of which there is none) that any current cheerleaders owe their position to past discrimination against blacks or Hispanics by the school district or its agents. Cf. Coalition to Save Our Children v. State Board of Education, supra, 90 F.3d at 768-69. To prevent children who are not beneficiaries of past discrimination from becoming cheerleaders, because of their race, is, on this record, a barefaced denial of equal protection.

The school district also challenges the breadth of the special master's authority. But this challenge is largely moot, or at least premature, in light of our rulings on the challenges to specific provisions of the decree. These rulings curtail the special master's authority in precisely those areas in which the school district complains about his uncanalized powers. The district has not complained about specific abuses of the powers of his that have not been challenged. When and if he abuses those powers, the district may seek a remedy.

What we have said so far disposes of portions of the cross-appeal by the plaintiffs--for example their argument that there should be separate quotas for black and Hispanic teachers, which we obviously reject; their argument that teachers (all of whom are Hispanic) in bilingual education programs should not count toward the quota for minority teachers, which is moot in light of our rejection of the quota; and their argument that Fund 12 should not be capped, which we have accepted. But there is more to the cross-appeal. Although the plaintiffs are not complaining about the decree's failure to impose a racial quota on special education programs for children suffering from behavioral disorders, they want the black students in these programs reevaluated to make sure they belong there and haven't been put there because of their race. But as there is no finding that this form of racial discrimination occurred, 851 F.Supp. at 1182-83, there is no basis for a remedial order concerning it, in the absence of a "fencing in" rationale that has not been argued.

We agree with the plaintiffs, however, that the magistrate judge erred in excluding preschool programs on the ground that preschoolers can't have been injured by past discrimination against minority students since by definition they were not students then. (This was not his only ground, but we cannot tell how important it was in his thinking.) Well, neither were first graders. Because kids grow up faster than school desegregation cases reach the remedy stage, there is never a close matching of the class discriminated against with the class benefited. To insist on such matching would be to abolish school desegregation litigation. Although the line must be drawn somewhere, it is arbitrary to draw it, as the magistrate judge did, between prekindergarten and kindergarten, without some better explanation than he offered. This provision of the decree, unlike the others that we have discussed (all but the provision relating to the master's powers), we do not reverse outright, but merely remand for reconsideration by the magistrate judge.

We come to the financing of the $48 million building program. The program is designed to facilitate integration by upgrading predominantly minority schools and building three new schools in predominantly minority neighborhoods. A common way in which local governments in Illinois finance such programs is by the issuance of a type of debt instrument called a "certificate of participation." This is similar in many respects to a bond but can be issued by a school district without a referendum. The magistrate judge ordered the school district to issue certificates of participation to finance the building program. In the background of the order is a decision by this court last summer that a suit which a number of Rockford residents had brought challenging the school district's authority under state law to finance its compliance with the decree out of the tort immunity fund belonged in state court. In re Application of County Collector, 96 F.3d 890 (7th Cir.1996). The district court had held that the school district was authorized to use the tort immunity fund for this purpose. Our action in vacating the decision cast a cloud over the school district's authority to do so, and thereby undermined the district's prospects of financing the building program through certificates of participation or any other sort of debt instrument, because the district had been looking to the tort immunity fund to service the debt. As we mentioned earlier, the district's authority under state law to levy other property taxes is limited.

It might seem quite enough for the decree to order the school district to do the building, and let the school district figure out where to get the money for it from. That would not be a case of ordering the district to do something beyond its control, for if it found itself stymied by state law the federal district court could as a last resort command the state to come up with the money. Missouri v. Jenkins, 495 U.S. 33, 57, 110 S.Ct. 1651, 1666, 109 L.Ed.2d 31 (1990); In re Application of County Collector, supra, 96 F.3d at 904; United States v. Board of Education, 11 F.3d 668, 673-74 (7th Cir.1993). But the court would of course be reluctant to do this, and reluctant also to be put in the position of having to do it by the school district's foot-dragging. The district court was therefore justified in ordering the school district to use a method of financing the building program that would avoid displacing the state's taxing authority into the federal court system.

We cannot see what as a practical matter the school district hopes to gain by appealing from this portion of the decree. It concedes that it has to find the $48 million for the building program; it doesn't have $48 million; it has to borrow it; certificates of participation are the method of borrowing that the school district itself prefers. If the district finds itself stymied by state law in selling or repaying the certificates of participation, it will have to ask the district court for relief. That court has the power, as we have just noted, though it is a power to be exercised sparingly, to require the state to come up with the money to fund a valid federal decree, whatever state law may provide. No purpose would be served by delaying the issuance of the certificates of participation to await, what may be years in coming, a definitive ruling on the lawfulness under state law of using the tort immunity fund as a source for repaying them.

Last and least is the school district's appeal, backed up by its petition for mandamus, challenging a brace of orders by the magistrate judge relating to the powers of the special master. A hearing was held on a proposal by him that the school district be ordered to buy a property for one of the programs required by the decree. The master, very curiously, participated with the aid of a lawyer and did party-like things like seeking and resisting discovery. The school district asked the magistrate judge to bar the special master from participating in this way in a further hearing on the order to buy the property. The magistrate judge refused, later remarking that the special master occupies "the position of a traditional litigator" in certain matters relating to the administration of the decree. Since a special master is an ad hoc judicial officer, his occupying the status of a party or "litigator," whatever exactly the magistrate judge meant by that, may certainly be questioned. E.g., In re Gilbert, 276 U.S. 6, 9, 48 S.Ct. 210, 211, 72 L.Ed. 441 (1928); Reed v. Cleveland Board of Education, 607 F.2d 737, 747 (6th Cir.1979). And we are mindful of the criticisms that have been made of the use of special masters in institutional reform litigation--a use that involves endowing a private individual with powers over state government. See, e.g., Linda J. Silberman, "Judicial Adjuncts Revisited: The Proliferation of Ad Hoc Procedure," 137 U. Pa. L.Rev. 2131, 2161-68 (1989). But we do not have jurisdiction over this appeal, and will not allow our lack of jurisdiction to be circumvented by the facile expedient of a petition for mandamus.

The further hearing was canceled because the order to buy the property was vacated. This development makes the school district's motion to bar the special master from participating in the hearing, and the appeal from the denial of the motion, thoroughly moot. In any event, the magistrate judge's orders allowing the special master to discover and be discovered, and otherwise to play the party role in the hearing, are not injunctions, and so are not appealable regardless of finality. They are merely procedural orders, and while such orders have the form of injunctions because they order a party to do or not to do something, they are for obvious reasons not treated as injunctions for purposes of determining appealability. Firestone Tire & Rubber Co. v. Risjord, 449 U.S. 368, 377-78, 101 S.Ct. 669, 675-76, 66 L.Ed.2d 571 (1981); United States v. Nixon, 418 U.S. 683, 690-91, 94 S.Ct. 3090, 3098-99, 41 L.Ed.2d 1039 (1974); Cobbledick v. United States, 309 U.S. 323, 60 S.Ct. 540, 84 L.Ed. 783 (1940); Central States, Southeast & Southwest Areas Pension Fund v. Express Freight Lines, Inc., 971 F.2d 5, 6 (7th Cir.1992); In re Establishment Inspection of Skil Corp., 846 F.2d 1127, 1129 (7th Cir.1988). Should any appealable order be issued after a hearing in which the special master participated in an irregular manner, the appellant if he was prejudiced by the irregularity can ask us to reverse on that basis.

To summarize, the comprehensive remedial order is affirmed in part and reversed in part, as indicated in this opinion, and the matter remanded for further proceedings consistent with this opinion; the financing orders are affirmed; the appeal from orders relating to the special master's participation in the canceled hearing is dismissed; and the petition for a writ of mandamus is denied.