
    ST. LOUIS FIRE FIGHTERS ASSOCIATION INTERNATIONAL ASSOCIATION OF FIRE FIGHTERS LOCAL 73; William Rudden; Edwin F. Libby; John F. Welch; Ralph E. Break; Michael T. Donovan; William O. Hill; William O. Smith; Irvin M. Sprous; Timothy V. Tyebo; Dwight C. Cross; Cecil E. Morris; Charles J. Zoeller; Timothy J. May; Ronald Gronemeyer; Mark R. Duffy, Plaintiffs-Appellants, v. CITY OF ST. LOUIS, MISSOURI, Defendant-Appellee, Firefighters’ Institute for Racial Equality; Charles Bates; Nathanial Sutherland; Joseph Jones; Gilbert Vaughn; Eugene Stanton; Roland Logan; Leroy Harris, Intervenors-Defendants-Appellees. ST. LOUIS FIRE FIGHTERS ASSOCIATION INTERNATIONAL ASSOCIATION OF FIRE FIGHTERS LOCAL 73; William Rudden; Edwin F. Libby; John F. Welch; Ralph E. Break; Michael T. Donovan; William O. Hill; William O. Smith; Irvin M. Sprous; Timothy V. Tyebo; Dwight C. Cross; Cecil E. Morris; Charles J. Zoeller; Timothy J. May; Ronald Gronemeyer; Mark R. Duffy, Plaintiffs-Appellees, v. CITY OF ST. LOUIS, MISSOURI, Defendant-Appellee, Firefighters’ Institute for Racial Equality; Charles Bates; Nathanial Sutherland; Joseph Jones; Gilbert Vaughn; Eugene Stanton; Roland Logan; Leroy Harris, Intervenors-Defendants-Appellants. FIREFIGHTERS’ INSTITUTE FOR RACIAL EQUALITY; Charles Bates; Nathanial Sutherland; Joseph Jones; Gilbert Vaughn; Eugene Stanton; Roland Logan; Leroy Harris, Cross Claimants-Appellants, v. CITY OF ST. LOUIS, MISSOURI, Cross Defendant-Appellee.
    Nos. 95-3782, 95-4011.
    United States Court of Appeals, Eighth Circuit.
    Submitted April 11, 1996.
    Decided Sept. 19, 1996.
    
      Jerome A Diekemper, St. Louis, MO, argued (Richard P. Perkins, on the brief), for appellant.
    Alif A. Williams, St. Louis, MO, argued, for appellee/cross-appellant.
    Michael A Garvin, St. Louis, MO, argued, (Kathleen G. Tanner, on the brief), for City of St. Louis.
    Before MAGILL and LOKEN, Circuit Judges, and GOLDBERG, Judge.
    
      
       THE HONORABLE RICHARD W. GOLDBERG, Judge, United States Court of International Trade, sitting by designation.
    
   MAGILL, Circuit Judge.

The St. Louis Fire Fighters Association International Association of Fire Fighters Local 73 and individual plaintiffs (Local 73) brought suit against the city of St. Louis (the City) under 42 U.S.C. § 1981 and Title VII of the Civil Rights Act of 1964, 42 U.S.C. §§ 2000e-l-2000e-17, alleging that the test results from a multiphased testing procedure for the promotion of fire captains to battalion chiefs in the City’s fire department was illegally reweighted in favor of African-Americans. The Firefighters’ Institute for Racial Equality and individual intervenors (FIRE) intervened as intervenor-defendants/cross-claim plaintiffs in the suit, challenging different aspects of the testing procedure as having an adverse impact on African-Americans. The district court granted a preliminary injunction to Local 73, enjoining the City from promoting fire captains to battalion chiefs on the basis of the promotion test battery results. The City subsequently announced that it would abandon the beleaguered testing procedures entirely, and would develop a new procedure for promotions. The district court dismissed Local 73’s claim and FIRE’s cross-claim as moot, denied Local 73’s motion for leave to file a third amended complaint requesting additional relief, and denied Local 73’s and FIRE’s motions for attorney’s fees and costs.

Local 73 appeals the district court’s (1) dismissal of its complaint as moot; (2) denial of its motion to file a third amended complaint; and (3) its denial of attorney’s fees and costs. FIRE cross-appeals only the district court’s denial of attorney’s fees and costs. We affirm the district court’s dismissal of Local 73’s complaint as moot and its denial of Local 73’s motion to file a third amended complaint. We reverse the district court’s denial of attorney’s fees and costs to Local 73 and FIRE as an abuse of discretion, and remand for a determination of reasonable attorney’s fees for both Local 73 and FIRE.

I.

In 1991, the City announced plans to implement a testing procedure to promote fire captains to battalion chiefs. The City communicated with both Local 73, a fire fighter labor organization, and FIRE, a civil rights organization pursuing the interests of African-American fire fighters, to create a generally acceptable testing procedure. Eventually, the City devised a three-part test battery, consisting of a written test, a fire scene test, and an assessment center test. The test battery was structured so that candidates had to pass each test in order to proceed to the next. The written test was administered in February 1992 to 54 candidates, 20 of whom were African-American. The fire scene test was administered in June 1993 to 34 candidates, 10 of whom were African-American. The assessment center test was administered in April 1994 to 23 candidates, 7 of whom were African-American.

In June 1993, after considering several schemes for weighting the multiphased test results, and after both Local 73 and FIRE objected to various formulations, the City proposed to make the written and fire scene tests pass/fail, and then to rank passing candidates solely according to their assessment center scores. Of the 23 candidates who took the assessment center test, African-Americans ranked eighth, eleventh, twelfth, seventeenth, eighteenth, twenty-second, and twenty-third. Upon considering these results, and contemplating possible litigation on the basis of an adverse impact against African-Americans, the City reweighted the test battery results. While keeping the written test pass/fail, the City made the fire scene test worth 30% of the ranking score, and made the assessment center worth 70% of the ranking score. Following this reweight-ing, white candidates tended to drop in the ranking, and African-American candidates, who now ranked third, fifth, eighth, eleventh, twelfth, eighteenth, and twenty-third, tended to improve in ranking.

Local 73 filed suit against the City on August 17, 1994, claiming a violation of employment discrimination laws on the basis of the reweighted scores. In its initial, first amended, and second amended complaints, Local 73 sought a temporary restraining order, a temporary injunction, and a permanent injunction barring the City from promoting fire captains to battalion chiefs on the basis of the disputed test procedure. FIRE intervened in the lawsuit, generally defending the City’s decision to reweight the test results. See, e.g., Intervenors’ Answer To Pis.’ Second Am. Compl. at ¶ 9, reprinted in II Appellant’s App. at 355 (denying Local 73’s allegation that City’s decision to re-weight scores was arbitrary and capricious, and designed only to change the rankings of the candidates based on their race). In a cross-complaint, however, FIRE alleged that the written test and assessment center test had an adverse impact against African-Americans, and sought permanent injunctive relief barring the City from making promotions based on the disputed test procedures.

The district court granted a temporary restraining order on August 17, 1994, and a preliminary injunction on September 15, 1994, barring the City from making promotions on the basis of the disputed test procedures. On February 14, 1995, prior to trial for permanent injunctive relief, the City cancelled the entire promotion test procedure, and declared that it would not base any promotions on the disputed test battery. Instead, the City announced its intention to establish a new testing procedure. See Def.’s Motion for Summ. J. at ¶ 3, reprinted in II Appellant’s App. at 330.

Construing the City’s motion for summary judgment as a motion to dismiss for mootness, the district court on March 13, 1995, held that Local 73’s complaint and FIRE’s cross-complaint were moot, and dismissed the actions. See Mem. Op. at 6. In reaching this decision, the district court found that, in light of the City’s explicit promise to abandon the disputed test procedures and not to base any promotions on the test battery results,

the Court is persuaded that there exists no likelihood of recurrence of the use of the tests of which intervenors’ pleading complains. ... The injunctive relief sought is mooted by the City’s cancellation of the challenged rankings. Plaintiffs’ belated invocation of a number of other types of relief which might have been sought, but were not, fails to undermine the conclusion that the relief actually prayed for is rendered meaningless by the City’s actions.

Id. at 4-5. The district court also found that “there exist no lingering effects of any alleged violations which are capable of redress by this Court.” Id. at 6. Noting that no promotions had been made based on the disputed procedures, the district court concluded that

[t]he Court has never been asked to determine which firefighters are entitled to promotion based on some lawfully-determined application of the test results which have been attacked by all the candidates; the cancellation of those results thus clears and levels the field on which all candidates will now compete, based on whatever new testing procedures are developed by the City. Regardless of the determination of the parties’ claims, the Court has never been in a position to prescribe the use of particular tests by the City, and the Court cannot pass on the legality of tests yet to be devised and implemented.

Id. In a separate order filed on October 3, 1995, the district court summarily denied a motion by Local 73 to alter or amend the order and judgment and for leave to file a third amended complaint.

Local 73 filed a motion seeking $68,090.00 in attorney’s fees and $8,613.89 in costs, while FIRE filed a motion seeking $66,181.25 in attorney’s fees and $22,397.57 in costs. On October 5, 1995, the district court denied these motions. Initially, the district court found that “whether plaintiffs and interve-nors qualify as prevailing parties ... is questionable at best,” Order at 3, because neither Local 73 nor FIRE “succeeded in preserving other aspects of the procedure which they defended,” id. at 2; because “neither group benefitted uniformly or [was] disadvantaged uniformly by any given change in the testing or scoring; [because it cannot] be said that the various individual plaintiffs and interve-nors are uniformly benefitted or disadvantaged by the cancellation of the previous results and the administration of a new promotion procedure,” id.; and because “inter-venors failed to obtain the injunctive relief which they sought.” Id. at 2-3.

Alternatively, assuming that Local 73 and FIRE were prevailing parties, the district court exercised its discretion and denied all attorney’s fees to both Local 73 and FIRE. The district court stated that:

Movants have failed entirely to take into account their minimal success in their requests for substantial fees and costs, and have failed to reflect their limited degree of success by requesting only partial fees or by making any attempt to distinguish fees and expenses incurred with respect to claims upon which the Court’s mootness determination does not constitute success.... [B]oth intervenors and plaintiffs seek total awards which, in the Court’s view, are grossly excessive for this seven-month litigation.

Id. at 3 (note omitted). Local 73 and FIRE now appeal.

II.

We review the district court’s dismissal for mootness de novo. See Stop H-3 Ass’n v. Dole, 870 F.2d 1419, 1423 (9th Cir.1989). A case is properly dismissed as moot if it “has lost its character as a present, live controversy of the kind that must exist if we are to avoid advisory opinions on abstract questions of law.” Princeton Univ. v. Schmid, 455 U.S. 100, 103, 102 S.Ct. 867, 869, 70 L.Ed.2d 855 (1982) (per curiam) (quotations and citation omitted) (holding that university’s amendment of regulation made moot a challenge to regulations).

Generally, the “voluntary cessation of allegedly illegal conduct does not deprive the tribunal of power to hear and determine the case, i.e., does not make the case moot.” United States v. W.T. Grant Co., 345 U.S. 629, 632, 73 S.Ct. 894, 897, 97 L.Ed. 1303 (1953). Where, however,

(1) it can be said with assurance that there is no reasonable expectation that the alleged violation will recur, and (2) interim relief or events have completely and irrevocably eradicated the effects of the alleged violation ... it may be said that the case is moot because neither party has a legally cognizable interest in the final determination of the underlying questions of fact and law.

County of Los Angeles v. Davis, 440 U.S. 625, 631, 99 S.Ct. 1379, 1383, 59 L.Ed.2d 642 (1979) (quotations and citations omitted). “The burden of demonstrating mootness ‘is a heavy one.’” Id. (quoting W.T. Grant Co., 345 U.S. at 633, 73 S.Ct. at 897-98).

We agree with the district court that both prongs of the Davis test have been met by the City in this case, and that the case was properly dismissed as moot. The disputed testing procedures have been abandoned by the City, and the district court found “that there exists no likelihood of recurrence of the use of the tests.” Mem. Op. at 4. While not disputing this finding, Local 73 argues that the City might possibly improperly manipulate the results of future tests. We decline to accept this attenuated possibility of future misdeeds as sufficient to warrant our continued jurisdiction, and conclude that this argument is simply too speculative to keep an otherwise moot controversy alive.

We also fail to see any persistent ill effects of the alleged wrongdoing in this case. Both Local 73 and FIRE were concerned that promotions would be made based on the results of the disputed test procedures, and the only relief requested by the parties was an injunction barring such promotions. No promotions were ever made based on the disputed testing procedures and, with the testing procedures abandoned, the requested relief is obviously unnecessary. In light of this, we conclude that the district court properly dismissed Local 73’s complaint and FIRE’s cross-complaint as moot.

III.

After its complaint was dismissed as moot, Local 73 moved for leave to file a third amended complaint, which was denied by the district court. We review this decision for abuse of discretion. See Egerdahl v. Hibbing Community College, 72 F.3d 615, 620 (8th Cir.1995).

“A district court may refuse to grant leave to amend if the plaintiff had an earlier opportunity to cure a defect in her complaint but failed to do so.” Id. In this case, the district court afforded Local 73 two opportunities to amend its pleadings during the course of proceedings. Both times Local 73 failed to add a request for damages or additional injunctive relief. Further, while a pretrial motion to amend pleadings should be liberally granted, “different considerations apply to motions filed after dismissal.” Humphreys v. Roche Biomedical Lab., Inc., 990 F.2d 1078, 1082 (8th Cir.1993). The Humphreys court stated that

a district court does not abuse its discretion in refusing to allow amendment of pleadings to change the theory of a case if the amendment is offered after summary judgment has been granted against the party, and no valid reason is shown for the failure to present the new theory at an earlier time.

Id. (quotations and citations omitted). Here, Local 73 waited until after the case was dismissed as moot before seeking leave to file a third amended complaint, and proffered no adequate reason explaining this delay. In these circumstances, we conclude that the district court did not abuse its discretion in denying Local 73’s motion to file a third amended complaint.

IV.

A.

Under 42 U.S.C. §§ 1988 and 2000e-5(k), prevailing parties in § 1981 and Title VII actions are entitled, at the district court’s discretion, to attorney’s fees. We review the district court’s determination of whether a litigant is a prevailing party de novo. See Oxford House-A v. City of Univ. City, 87 F.3d 1022, 1024 (8th Cir.1996); cf. Marquart v. Lodge, 26 F.3d 842, 844 (8th Cir.1994).

This Court has recognized the “catalyst” theory of prevailing parties:

Where a defendant voluntarily complies with a plaintiffs requested relief, thereby rendering the plaintiffs lawsuit moot, the plaintiff is a “prevailing party” under section 1988 if his suit is a catalyst for the defendant’s voluntary compliance and the defendant’s compliance was not gratuitous, meaning, the plaintiffs suit was neither frivolous, unreasonable nor groundless.

Little Rock Sch. Dist. v. Special Sch. Dist. 1, 17 F.3d 260, 262 (8th Cir.1994) (quotations and citations omitted); see also A.J. by L.B. v. Kierst, 56 F.3d 849, 865 (8th Cir.1995) (“Plaintiffs, thus, may ‘prevail’ under section 1988 if they succeed on any significant issue in litigation which achieves some of the benefit the parties sought in bringing suit, despite the absence of a formal judgment in their favor.” (quotations and citations omitted)).

In this case, both Local 73 and FIRE succeeded in preventing any promotions from fire captain to battalion chief from being made based on the test procedures which they disputed. We believe that this was a significant issue in the case; indeed, this was all that either party had specifically requested. Nor is there any disagreement that the litigation by Local 73 and FIRE was the catalyst for the City’s abandonment of the disputed test procedures; at oral argument, the City acknowledged that the litigation, referred to as “pressure on both sides,” caused the City’s abandonment of the test procedures.

Finally, we cannot say that the City’s action was gratuitous. While we have no opinion on what the merits of the case might have been had it proceeded to trial and judgment, we do not believe that either Local 73’s complaint or FIRE’s cross-complaint were frivolous, unreasonable, or groundless. 42 U.S.C. § 2000e-2(£) provides that an employer may not “adjust the scores of ... or otherwise alter the results of, employment related tests on the basis of race.... ” FIRE presented evidence that the City set the passing score for the fire scene test to avoid disadvantaging white candidates, while Local 73 presented evidence that the City reweighted the scores of the fire scene test and assessment center test components to avoid disadvantaging African-American candidates. Whether this evidence would have been accepted as correct by a finder of fact and whether, if accepted, these facts would have constituted a violation of § 2000e-2(i) are questions not before us; clearly, however, they raise reasonable issues of law which could have been decided against the City.

B.

While we review a district court’s award of attorney’s fees for abuse of discretion, see Bass v. Southwestern Bell Tel., Inc., 817 F.2d 44, 46 (8th Cir.1987), a district court’s discretion to deny attorney’s fees to a prevailing party is narrow. See Little Rock Sch. Dist., 17 F.3d at 262. Rather, “[prevailing parties ordinarily should recover section 1988 fees unless special circumstances would make such an award unjust.” Id. at 262-63. See also Hatfield v. Hayes, 877 F.2d 717, 719 (8th Cir.1989) (“Absent special circumstances, a prevailing party should be awarded section 1988 fees as a matter of course.” (quotations and citation omitted, emphasis in original)).

Although the factors cited by the district court are relevant to determining a reasonable attorney’s fees award, we hold that they do not constitute sufficiently “special circumstances” to justify a complete denial of any award. See, e.g., Hatfield, 877 F.2d at 720 (citing cases). While “§ 1988 contemplates the denial of fees to de minim-is victors,” Farrar v. Hobby, 506 U.S. 103, 117, 113 S.Ct. 566, 576, 121 L.Ed.2d 494 (1992) (O’Connor, J., concurring), this is not a fair assessment of Local 73’s and FIRE’s success in this case. Although neither Local 73 nor FIRE were able to secure promotions for the individual plaintiffs and intervenors, the parties never requested this relief. While certain individual plaintiffs and inter-venors, who now must await future opportunities for promotion, might have been promoted to battalion chief had the City been allowed to proceed based on the disputed test procedures, we do not see this as a pyrrhie victory justifying the denial of attorney’s fees. See id. Rather, we presume that all parties were sincere in their efforts to secure nondiseriminatory employment practices for all promotion candidates.

We therefore must remand this case to the district court for a determination of reasonable attorney’s fees awards to both FIRE and Local 73. In doing so, however, we note that the district court retains discretion in determining what constitutes a reasonable award in the circumstances of this case, and that we share many of the district court’s concerns regarding the parties’ original fee requests. As found by the district court, the sums originally requested by the parties are grossly excessive, and should be adjusted to reflect the success achieved by the parties. See Farrar, 506 U.S. at 114, 113 S.Ct. at 574 (“the most critical factor in determining the reasonableness of a fee award is the degree of success obtained” (quotations and citation omitted)).

We also note that it would be unjust to make the City accountable for costs incurred by Local 73 and FIRE in supporting the City’s position and defending various aspects of the test procedures against the other party. See, e.g., Bigby v. City of Chicago, 927 F.2d 1426, 1428 (7th Cir.1991) (“a Title VII defendant’s fee liability would not extend to fees associated with the defense of third party interests”); Reeves v. Harrell, 791 F.2d 1481, 1484 (11th Cir.1986) (defendant not liable for prevailing party’s defense against third party), cert. denied, 479 U.S. 1033, 107 S.Ct. 880, 93 L.Ed.2d 834 (1987). If, upon rehearing, the district court determines that Local 73 and FIRE took conflicting, nonfirivolous positions in this case, we believe that it would be proper for the district court to determine one reasonable fee for the litigation to date, and to split that fee among the two opposing sides according to their relative success.

V.

For the foregoing reasons, we affirm the district court’s dismissal of Local 73’s complaint and FIRE’s cross-complaint as moot, and we affirm the district court’s denial of Local 73’s motion for leave to file a third amended complaint. We reverse the district court’s determination that Local 73 and FIRE were not prevailing parties, and we reverse and remand the district court’s denial of attorney’s fees and costs to Local 73 and FIRE. 
      
      . Individual plaintiffs are fifteen white St. Louis fire captains who have taken the battalion chief promotion test battery.
     
      
      . Individual intervenors are seven African-American St. Louis fire captains who took the battalion chief promotion test battery.
     
      
      . African-American candidates tended to perform better than white candidates in the fire scene test, while white candidates tended to perform better in the assessment center test. Because of this, lowering the score to pass on the fire scene test tended to benefit white candidates more than African-American candidates. William Duffe, the City’s personnel director, testified that he considered the possibility of litigation by adversely affected whites if a high passing score for the fire scene test was set, see II Prelim. Inj. Hr'g Tr. at 56, and testified that "[w]e lowered the passing point to a level where the adverse impact against the white candidates was minimized.” Id. at 54.
     
      
      . Eight white candidates dropped in ranking due to the reweighting of the test scores, while three improved. The rankings of four white candidates were not affected by the reweighting of the test scores.
     
      
      . The district court also noted that the fee requests failed to specify which adverse party should be assessed fees and costs: "given the fact that plaintiffs and intervenors were adversaries in the litigation, it is conceivable that any fee award in favor of one group should be assessed, at least in part, against the other.” Order at 2.
     
      
      . Local 73 argues that despite its failure to request injunctive relief promoting individual plaintiffs, compensatory damages, or other additional relief, the district court was obligated under Federal Rule of Civil Procedure 56(c) to award such appropriate relief. We disagree. As noted by the Supreme Court in Albemarle Paper Co. v. Moody, 422 U.S. 405, 424, 95 S.Ct. 2362, 2374-75, 45 L.Ed.2d 280 (1975), "a party may not be 'entitled’ to relief if its conduct of the cause has improperly and substantially prejudiced the other parly.... To deny back pay because a particular cause has been prosecuted in an eccentric fashion, prejudicial to the other party, does not offend the broad purposes of Title VII." (emphasis in original). In its own Title VII action, Local 73 waited until after the City had made substantial changes in its hiring practices and after the case had been dismissed as moot before requesting a broad range of new remedies, the source of which was not obvious in its original pleadings and prosecution of its cause. In these circumstances, we do not believe that the mere potential of unrequested remedies could have allowed the district court to maintain jurisdiction in this matter.
     
      
      . In determining that neither FIRE nor Local 73 were prevailing parties, the district court relied, in part, on the definition of "prevailing party” provided by the Supreme Court in Farrar v. Hobby, 506 U.S. 103, 113 S.Ct. 566, 121 L.Ed.2d 494 (1992). See Order at 3. In Little Rock School District v. Special School District 1, 17 F.3d 260, 263 n. 2 (8th Cir.1994), we specifically declined to extend this definition "beyond its context of determining prevailing party status after a final determination on the merits of litigation.”
     
      
      . In addition, the district court found that plaintiffs had demonstrated a likelihood of success sufficient to grant plaintiffs first a temporary restraining order and later a preliminary injunction against the City to prevent it from promoting candidates based on the disputed test procedures. See Order Granting T.R.O. at 2, reprinted in Appellant's App. at 47; Order Granting Prelim. Inj. at 5, reprinted in II Appellant’s App. at 261. We cannot, consistent with these findings, conclude that the plaintiffs' complaint was frivolous.
     
      
      . The district court expressed concern that:
      Apparently unmindful of the Supreme Court's admonition that fee awards are not intended to " 'produce windfalls to attorneys,’ " Riverside v. Rivera, 477 U.S. 561, 580, 106 S.Ct. 2686, 2697, 91 L.Ed.2d 466 (1986) (citation omitted), plaintiffs seek fees at an hourly rate greater than that reflected in their agreement with counsel....
      Order at 3. We do not believe that the hourly rate previously agreed upon by a party with its counsel is dispositive for determining a reasonable award of attorney’s fees. Cf. Blanchard v. Bergeron, 489 U.S. 87, 93, 109 S.Ct. 939, 944, 103 L.Ed.2d 67 (1989) ("a contingent-fee contract does not impose an automatic ceiling on an award of attorney's fees”). We note, however, that such a previously agreed upon fee may well be strongly indicative of what constitutes a "reasonable” fee, see, e.g., Winter v. Cerro Gordo County Conservation Bd., 925 F.2d 1069, 1074 (8th Cir.1991) (award of attorney's fees based on fee agreement), and may properly be considered by the district court in its analysis.
     
      
      . In determining a reasonable attorney's fee, the district court should consider:
      (1) the time and labor required; (2) the novelty and difficulty of the questions; (3) the skill requisite to perform the legal service properly; (4) the preclusion of employment by the attorney due to acceptance of the case; (5) the customary fee; (6) whether the fee is fixed or contingent; (7) time limitations imposed by the client or the circumstances; (8) the amount involved and the results obtained; (9) the experience, reputation, and ability of the attorneys; (10) the “undesirability” of the case; (11) the nature and length of the professional relationship with the client; and (12) awards in similar cases.
      
        Winter, 925 F.2d at 1074 n. 8.
     