SELYA, Circuit Judge.

Thirty-five white male applicants for positions in the Boston Fire Department (the Department) filed suit in the district court on September 14, 1989. The plaintiffs alleged that a bevy of named defendants, including the City of Boston, various municipal officials, and the state personnel administrator, discriminated against them on the basis of race both in constituting an eligibility list and in making appointments to positions within the Department by means of the list. The district court granted summary judgment for the defendants. We affirm.

I. BACKGROUND

The two original suits described in note 1, supra, resulted in the entry of the so-called Beecher decree. See Boston Chapter, NAACP, Inc. v. Beecher, 371 F. Supp. 507, 520-23 (D.Mass.), aff'd, 504 F.2d 1017 (1st Cir. 1974), cert. denied, 421 U.S. 910, 95 S.Ct. 1561, 43 L.Ed.2d 775 (1975). Since 1974, the hiring of firefighters in much of Massachusetts has been circumscribed by this decree. Over time, the decree has been supplemented by several consent decrees designed to implement administrative procedures for offering examinations, establishing eligibility lists, releasing municipalities from continuing judicial oversight, and the like. We understand the plaintiffs to be challenging both the Beecher decree and the consent decrees entered to effectuate it. In general, however, we will refer to the decree in the singular, since it is the Beecher decree that is the cynosure of the parties' arguments.

Unlike some 30-odd other fire departments which heretofore met the goals of the decree and gained release from its constraints, the City of Boston remains under its aegis. In 1987, the state personnel administrator, acting on behalf of the Department, conducted a written examination for the position of firefighter. The personnel administrator then complied an eligibility list which have preferential standing to blacks and Spanish-surnamed individuals. Despite the fact that all 35 appellants earned perfect scores on the 1987 examination, they were ranked below several minority candidates who earned lower scores. As a result, appellants were disadvantaged with respect to vacant firefighter positions.

In the district court, appellants sought a salmagundi of relief, including an order placing their names at the top of the certified eligibility list and an injunction prohibiting continued preferential treatment of black and Spanish-surnamed persons in connection with available firefighting jobs. They contended that Boston had met the decree's objectives because, in 1989, the Department had achieved a percentage of black and Spanish-surnamed members higher than the percentage of such minorities in Boston's general population at the time the decree was originally entered. Appellants also claimed that, to the extent anything remained to be done, the decree's ameliorative purposes could be satisfactorily accommodated without any affirmative action because the 1987 entrance examination for firefighters was race-neutral. Finally, appellants charged that the decree swept too broadly and, therefore, should not be enforced.

In due course, both sides moved for summary judgment. The district court denied the plaintiffs' motion and granted the defendants' motion. At that point, plaintiffs switched gears, moving for reconsideration on completely different grounds. The district court denied the motion. On appeal, plaintiffs protest both the entry of summary judgment and the ensuing refusal to reconsider.

II. THE LEGAL LANDSCAPE

It is clear that, when a judicial decree affording race-conscious relief is challenged, the decree must be subjected to strict scrutiny. See City of Richmond v. J.A. Croson Co., 488 U.S. 469, 494, 109 S.Ct. 706, 721, 102 L.Ed.2d 854 (1989) (plurality opinion); Wygant v. Jackson Bd. of Educ., 476 U.S. 267, 273, 106 S.Ct. 1842, 1846, 90 L.Ed.2d 260 (1986) (plurality opinion). Such scrutiny requires a reviewing court to vouchsafe that the relief is both warranted by a strong state interest and narrowly tailored to further that interest. See Stuart v. Roache, 951 F.2d 446, 449 (1st Cir. 1991), cert. denied, ___ U.S. ___, 112 S.Ct. 1948, 118 L.Ed.2d 553 (1992). It cannot be gainsaid that, when a race-conscious employment initiative is reasonably necessary to remedy the effects of past discrimination practiced by a public employer, a compelling state interest exists. See United States v. Paradise, 480 U.S. 149, 167, 107 S.Ct. 1053, 1064, 94 L.Ed.2d 203 (1987) (plurality opinion); Stuart, 951 F.2d at 449. In this case, appellants do not argue that the original finding of discrimination was flawed. Rather, their focus is on the continuing need for affirmative action, and particularly, the need for the type and kind of affirmative action required by the Beecher decree.

Along those lines, we believe that district courts should be flexible in considering requests for relaxation of, or release from, decrees which were initially established to bring about needed institutional reforms. See Rufo v. Inmates of Suffolk County Jail, ___ U.S. ___, 112 S.Ct. 748, 760, 116 L.Ed.2d 867 (1992) (considering motion to modify a consent decree). In the context of civil rights litigation, a central consideration in determining whether to dissolve structural remedies is whether the agency in question has come into compliance with constitutional requirements. Put another way, an inquiring court should ask whether the goals of the litigation, as incorporated in the outstanding decree, have been completely achieved. Board of Educ. v. Dowell, ___ U.S. ___, 111 S.Ct. 630, 636-37, 112 L.Ed.2d 715 (1991). Moreover, federal courts, in mulling whether to relax or abandon their supervision over the operation of local governmental units, should take federalism concerns into account, ever mindful that the "legal justification for displacement of local authority . . . is a violation of the Constitution by the local authorities." Id. 111 S.Ct. at 637. An intrusion by a federal court into the affairs of local government should be kept to a bare minimum and not be allowed to continue after the violation has abated and its pernicious effects have been cured.

To the extent that the plaintiffs here are seeking relaxation of one or more consent decrees, see supra p. 1274, it must be remembered that "a party seeking modification of a consent decree bears the burden of establishing that a significant change in circumstances warrants a revision of the decree." Rufo, 112 S.Ct. at 760. That party "may meet its initial burden by showing either a significant change in factual conditions or in law." Id. Dissolution or relaxation of a consent decree may be justified in a variety of circumstances, for example, when "changed factual conditions make compliance with the decree substantially more onerous." Id.; see also id. 112 S.Ct. at 760-63 (listing other bases for modifying or dissolving a consent decree in the context of an institutional reform case).

III. ANALYSIS

It is against this backdrop that we turn to appellants' asseverational array. We treat serially with appellants' three main arguments. We then deal in one fell swoop with the exhortations contained in the motion for reconsideration.

A.

Positing that the decree contemplates no more than the achievement of minority representation in the Department commensurate with the percentage of minorities resident in Boston at the time the decree was entered, appellants assert that the Department has already reached this modest pinnacle. Even assuming that the factual premise anent the Department's present composition is true, this postulate tortures the language of the decree, disregards the parties' consistent practice while operating under the decree, and defies common sense.

First, the relevant language of the decree is most naturally read as referring to contemporaneous population figures: "As a city or town achieves a complement of minorities commensurate with the percentage of minorities within the community, certification will be made according to existing Massachusetts law." Beecher, 371 F. Supp. at 523. Had the district court and the existing parties intended to embody in the decree a stipulation that a community would be released from the prescribed procedures upon reaching a complement of minorities commensurate with the percentage of minorities within the community in 1974, we feel confident that the decree would have said so.

Second, the undisputed evidence concerning practice under the decree indicates beyond hope of contradiction that applications for the release of municipalities from the decree's burdens have universally been guided by reference to contemporaneous population statistics. Few things evidence a decree's meaning more persuasively than an immutable, decade-old pattern of past practice under the decree, consensually engaged in by all sides in the underlying litigation that produced the decree.

Third, common sense suggests that it would be whimsical to peg parity ratios to obsolete population figures in this sort of context. The logical extension of appellants' argument is that a locality could not be freed from the decree's requirements even if its minority population dropped precipitously, to the point where the percentage of minority firefighters in service far exceeded the current percentage of minorities in the relevant population, as long as the percentage of minority firefighters remained lower than the 1974 percentage. We think it is farfetched to assume that the district court or the parties intended the decree to work in so quirky a fashion.

In addition to the obvious practical problems with using outdated statistics, there are also sound legal reasons for reading the terms of the decree to refer to current population levels. One implication of the recent Supreme Court school desegregation decisions is that federal courts, at least in the minerun of civil rights and institutional reform cases, have no choice but to make decisions about the maintenance, modification, or dissolution of structural remedial orders by referring to the most current population statistics readily available. After all, knowledge of demographic shifts is essential for determining whether patterns of minority representation in state institutions and organizations reflect state action, which has constitutional implications, or private preferences, which, generally, do not. See, e.g., Freeman v. Pitts, ___ U.S. ___, 112 S.Ct. 1430, 1437-38, 1447-48, 118 L.Ed.2d 108 (1992). We think that the plaintiffs' effort to cling to 1974 statistics, notwithstanding the availability of supervening census data, contradicts Freeman's teachings.

In sum, achieving parity in 1974 terms, without more, was not a particularly significant datum. In any event, it did not serve, in 1989, as a legally sufficient basis for defenestrating the Beecher decree.

B.

Next, appellants contend that the decree was satisfied because the qualifying examination that they passed was validated under EEOC guidelines and was, therefore, nondiscriminatory. This argument overlooks the language of the decree itself. Even a cursory reading makes it crystal clear that validated examinations are not an end in themselves but merely a means toward achieving the decree's actual objective: rough parity (to remedy the effects of past discrimination). See, e.g., Beecher, 371 F. Supp. at 522 ("Subsequent to obtaining the results of a valid examination, the defendant . . . shall promptly commence certifying applicants as eligible for appointment [in the manner directed by the decree] . . . ."); id. at 522-23 (specifying that the "hiring procedure shall apply to all future eligibility lists established subsequent to a valid firefighter entrance examination"). The argument to the contrary is a mere heuristic.

C.

The appellants also hawk the idea that, even if the goals of the Beecher decree have not yet been accomplished, the decree is constitutionally infirm because it sweeps too broadly. This argument is by no means a new one. Over 15 years ago, we found the decree to be narrowly tailored toward the achievement of its legitimate objectives. See Beecher, 504 F.2d at 1027 (judging the decree to be "carefully limited in extent and duration"). To be sure, in the intervening years the tests for determining whether remedial race-conscious relief is, in fact, narrowly tailored have been refined and clarified. See, e.g., Paradise, 480 U.S. at 177-79, 107 S.Ct. at 1069-71 (plurality opinion); Stuart, 951 F.2d at 453-55. But, that process of refinement and clarification does nothing to call the adequacy of the instant decree into serious question.

We will not wax longiloquent. In determining whether or not an order is narrowly tailored, a significant measure of deference is owed to the trial court's conclusion that a particular kind of relief is essential to heal a constitutional wound. See Paradise, 480 U.S. at 183, 107 S.Ct. at 1072-73 (plurality opinion). The district court, unlike the court of appeals, "has firsthand experience with the parties and is best qualified to deal with the 'flinty, intractable realities of day-to-day implementation of constitutional commands.'" Id. at 184, 107 S.Ct. at 1073 (citation omitted). While a district court's discretion is not unbridled, a reviewing court, in assessing whether a remedy is narrowly tailored, must bear in mind that the fashioning of a structural decree, like the decision as to whether to modify or dissolve it, is at bottom an exercise of equitable power. See Freeman, 112 S.Ct. at 1444. Given this deferential standard of review, appellants are whistling past the graveyard — albeit whistling rather loudly — in inveighing against the reach of the decree's remedial provisions.

In assessing an overbreadth challenge to an order directing race-conscious relief in the context of public employment, a court should consider, inter alia, the extent to which (i) the beneficiaries of the order are specially advantaged, (ii) the legitimate expectancies of others are frustrated or encumbered, (iii) the order interferes with other valid state or local policies, and (iv) the order contains (or fails to contain) built-in mechanisms which will, if time and events warrant, shrink its scope and limit its duration. The Beecher decree passes this test with flying colors.

In this case, only qualified minority candidates are specially advantaged; no minority candidate is placed on the eligibility list unless he or she has attained a passing score on the entrance examination. This is an important indicium of narrow tailoring. See Stuart, 951 F.2d at 454. Relatedly, the decree does not require that minority aspirants be appointed, nor does it dispense with the statutory preferences mandated by state law. Thus, the decree gives only a limited advantage, not a guarantee of employment, to minority applicants. This, too, is a significant factor. See Johnson v. Transportation Agency, 480 U.S. 616, 638, 107 S.Ct. 1442, 1455, 94 L.Ed.2d 615 (1987) (approving affirmative action plan because, among other things, rather than mandating quota hiring, it "merely authorize[d] that consideration be given to affirmative action concerns when evaluating qualified applicants"). As a result of these features, it can appropriately be said that the Beecher decree "is not being used simply to achieve and maintain racial balance, but rather as a benchmark against which the court could gauge . . . efforts to remedy past discrimination." Local 28, Sheet Metal Workers' Int'l Ass'n v. EEOC, 478 U.S. 421, 477-78, 106 S.Ct. 3019, 3051, 92 L.Ed.2d 344 (1986) (plurality opinion).

Moreover, the failure to appoint more high-scoring white applicants under the decree disturbs no legitimate, firmly rooted expectations on the part of those applicants. The record shows that, when appellants sought appointment to the Department, there were many white candidates with statutory preferences and perfect tests scores, and few firefighters' vacancies. Hence, irrespective of the decree, appellants could not reasonably have felt assured that they would be appointed. This factor, too, counsels in favor of upholding the decree. See Stuart, 951 F.2d at 454.

Finally, the decree's life is limited, remaining in force only until its requirements have been met. See Beecher, 371 F. Supp. at 523 (providing for release from appointment process mandated by the decree "[a]s a city or town achieves a complement of minorities commensurate with the percentage of minorities within the community"). Limitations of this sort are crucial factors in deflecting overbreadth challenges. See Stuart, 951 F.2d at 454. Indeed, the proof of the present pudding is that, since 1974, more than fifty percent of the communities originally affected by the decree have already been freed from further oversight.

Mindful of these realities, we conclude that the Beecher decree is tailored with sufficient precision to withstand the appellants' imprecations.

D.

On the motion for reconsideration, appellants unsuccessfully attempted to raise two additional arguments. They claimed, first, that the Department's achievements under the decree should be measured not by reference to the census figures for black and Spanish-surnamed individuals in the general population, but by reference to the census of such persons age 18 or older, thus dovetailing more snugly with the relevant labor pool. They also suggested that blacks and Spanish-surnamed individuals should be considered separately; and that, therefore, black aspirants should not be entitled to a continuing preference as Boston had exceeded the decree's goals with respect to black fire-fighters.

We need not dwell on the substance of these arguments. It is settled law that, once a motion to dismiss or a motion for summary judgment has been granted, the district court has substantial discretion in deciding whether to reopen the proceedings in order to allow the unsuccessful party to introduce new material or argue a new theory. See Mariani-Giron v. Acevedo-Ruiz, 945 F.2d 1, 3 (1st Cir. 1991); United States v. 5 Bell Rock Road, 896 F.2d 605, 611 (1st Cir. 1990); Appeal of Sun Pipe Line Co., 831 F.2d 22, 25 (1st Cir. 1987), cert. denied, 486 U.S. 1055, 108 S.Ct. 2821, 100 L.Ed.2d 922 (1988); Polyplastics, Inc. v. Transconex, Inc., 827 F.2d 859, 864 n. 4 (1st Cir. 1987); Pagan v. American Airlines, Inc., 534 F.2d 990, 992-93 (1st Cir. 1976). Consequently, we will overturn the trial court's decision on such a matter only if an appellant can persuade us that the refusal to grant favorable reconsideration was a clear abuse of discretion. Sun Pipe Line, 831 F.2d at 25; Pagan, 534 F.2d at 993.

Here, there is not so much as a whisper of a hint of an intimation of an abuse of discretion. The statistics upon which appellants belatedly sought to rely (in order to show a more precisely defined labor pool) were available to them all along. Moreover, those statistics, fairly read, likely tell a different story than appellants intend to convey. The most pertinent "labor pool" information that can be gleaned from the 1980 census figures is the head count of black and Spanish-surnamed individuals who were ten years of age, or older, in 1980 — a number which would give some approximate indication of the number of black and Spanish-surnamed individuals who, in 1989, were old enough to be considered for firefighters' positions. Based on those figures, a continuing lack of parity in the Department is statistically evident.

Appellants' other "new" argument — that the percentage figures for black and Spanish-surnamed individuals should be dismembered, so that once parity with the percentage of blacks in the labor force is achieved, the decree's guidelines for certifying blacks to the eligibility list should be lifted — fares no better. Once again, the argument relied on information that was available well before the time suit was started. Moreover, such an approach clearly contradicts the format of the original litigation, which constituted combined classes of black and Spanish-surnamed persons, not separate black and Spanish-surnamed classes. It also contradicts the clear intent of the decree and an unbroken skein of preexisting practice under the decree's terms.

When the losing party seeks reconsideration of an adverse judgment on a neoteric theory, factors such as due diligence and likelihood of success must weigh heavily in the balance. Where, as here, the movants' newly emergent arguments seem weak and the movants have offered no viable excuse for not advancing those arguments in a timely fashion when the parties crossmoved for summary judgment, we are unable to discern any principled basis on which the district court's denial of the motion for reconsideration might be overturned. In this case, as in most similarly postured cases, the district court's refusal to allow appellants the opportunity to revisit the barn after the horse has departed cannot be considered an abuse of discretion.

Affirmed.