
    OHIO-SEALY MATTRESS MANUFACTURING COMPANY, Sealy Mattress Company of Houston, Sealy Mattress Company of Puerto Rico, Inc., Sealy of the Northeast, Inc., and Sealy Mattress Company of Georgia, Inc., Plaintiffs-Appellees, Cross-Appellants, v. SEALY INCORPORATED, Sealy Spring Corporation-Indiana, Sealy Spring Corporation-East, Sealy Spring Corporation-West, Sealy Mattress of Colorado, Inc., Sealy Mattress Company of Northern California, Inc., Sealy Mattress Company of Southern California, Inc., Schnoor Manufacturing Company, Inc., Sealy Mattress Company of Florida, Inc., Sealy Mattress Company of Pittsburgh, Inc., and Sealy Mattress Company of Philadelphia, Inc., Defendants-Appellants, Cross-Appellees.
    Nos. 84-2886, 84-2926.
    United States Court of Appeals, Seventh Circuit.
    Argued June 6, 1985.
    Decided Oct. 21, 1985.
    
      Frederic F. Brace, Jr., Brace & O’Donnell, Chicago, 111., for defendants-appellants, cross-appellees.
    Phil C. Neal, Friedman & Koven, Chicago, 111., for plaintiffs-appellees, cross-appellants.
    Before CUMMINGS, Chief Judge, WOOD, Circuit Judge, and WRIGHT, Senior Circuit Judge.
    
    
      
       The Honorable Eugene A. Wright, Senior Circuit Judge of the United States Court of Appeals for the Ninth Circuit, is sitting by designation.
    
   HARLINGTON WOOD, Jr., Circuit Judge.

This is an appeal from an award of attorneys’ fees in a seemingly unending private antitrust action that has come to be referred to as “Ohio I.” See Ohio-Sealy Mattress Manufacturing Co. v. Kaplan, 745 F.2d 441, 443-46 (7th Cir.1984) (Ohio II case giving description of Ohio I litigation), (U.S. appeal pending); Ohio-Sealy Mattress Manufacturing Co. v. Duncan, 714 F.2d 740 (7th Cir.1983) (Ohio III), cert. denied, 464 U.S. 1044, 104 S.Ct. 712, 79 L.Ed.2d 176 (1984); Ohio-Sealy Mattress Manufacturing Co. v. Kaplan, 712 F.2d 270 (7th Cir.), cert. denied, 464 U.S. 1002, 104 S.Ct. 509, 78 L.Ed.2d 698 (1983); Ohio-Sealy Mattress Manufacturing Co. v. Sealy, Inc., 669 F.2d 490 (7th Cir.), cert. denied, 459 U.S. 943, 103 S.Ct. 257, 74 L.Ed.2d 201 (1982); Ohio-Sealy Mattress Manufacturing Co. v. Sealy, Inc., 585 F.2d 821 (7th Cir.1978), cert. denied, 440 U.S. 930, 99 S.Ct. 1267, 59 L.Ed.2d 486 (1979). The district court determined that the plaintiff (“Ohio-Sealy”) paid its attorneys approximately $1,295,924 for hours reasonably spent on issues on which the plaintiff prevailed. The district court then multiplied this figure by two to compensate plaintiff for the time-value of money and for inflation. Finally, the court rounded off the fee award to $2.6 million in order to be fair to the plaintiff in light of all the uncertainties of the fee calculation. The defendant (“Sealy”) appeals, arguing that a multiplier is inappropriate when the plaintiff compensated its attorneys on an hourly basis rather than on a contingency basis. The plaintiff cross-appeals, claiming that the district court underestimated the value of its attorneys’ services. We affirm in part, reverse in part, and remand.

I.

Section 4 of the Clayton Act provides that a person injured by an antitrust violation “shall recover threefold the damages by him sustained, and the cost of suit, including a reasonable attorney’s fee.” 15 U.S.C. § 15 (1982). A plaintiff who substantially prevails in an action for injunctive relief under the antitrust laws also recovers “the cost of suit, including a reasonable attorney’s fee.” 15 U.S.C. § 26 (1982). Although the successful antitrust plaintiff recovers attorneys’ fees as a matter of right, the plaintiff bears the burden of establishing the amount of compensable attorney time. See Spray-Rite Service Corp. v. Monsanto Co., 684 F.2d 1226, 1249 (7th Cir.1982), aff'd, 465 U.S. 752, 104 S.Ct. 1464, 79 L.Ed.2d 775 (1984); see also Hensley v. Eckerhart, 461 U.S. 424, 437, 103 S.Ct. 1933, 1941, 76 L.Ed.2d 40 (1983). The determination of what constitutes reasonable attorneys’ fees lies in the sound discretion of the district court, and we will disturb the district court award only for an abuse of that discretion. See Illinois v. Sangamo Construction Co., 657 F.2d 855, 862 (7th Cir.1981).

In this case, the plaintiff suggested an attorneys’ fees award of more than $17 million. It based this request on evidence that its lawyers, law clerks, and paralegals worked a total of 41,072.30 hours. OhioSealy asked that the court base the award of the attorneys’ then-current (1983) hourly rates, yielding a fee request of $4,331,-997.00, and that the court also apply a multiplier of 4 to compensate plaintiff for accepting “the risk of not prevailing, and therefore the risk of not recovering any attorney’s fees.” The defendant, needless to say, thought $17 million was a bit too much.

The district court first analyzed the hours claimed by plaintiff for the damages portion of this litigation and disallowed, among other things, hours devoted to an arbitration that Ohio-Sealy requested and lost, hours spent on two unsuccessful claims, and hours the court deemed attributable to excessive advocacy. The district court then examined the hours spent on Ohio-Sealy’s claims for equitable relief. Ohio-Sealy had obtained a decree enjoining Sealy from enforcing a number of provisions in the license agreement and from taking other specified acts. The decree did not, however, enjoin Sealy from enforcing the exclusive manufacturing provision of the agreement, and it did not order Sealy to divest the Florida, Philadelphia, and Pittsburgh licenses. The district court concluded that Ohio-Sealy had prevailed on only seventy-five percent of the issues relevant to equitable relief and therefore disallowed twenty-five percent of the hours claimed in connection with the first equitable relief proceeding, the appeal, and the second proceeding.

To determine a reasonable attorneys’ fees award, the district court started with the total dollar amount claimed at historical hourly rates. The court then obtained a weighted average historical hourly rate by dividing the total dollar amount claimed (based on historical rather than current hourly rates) by the total number of hours claimed. This procedure resulted in weighted average historical hourly rates of $52 per hour for attorneys and $20 per hour for paralegals. The court multiplied these average rates by the number of hours allowed, producing a base figure of $1,524,616. The court reduced this figure by fifteen percent “[d]ue to the overall vagueness of the plaintiff’s petitions, the inconsistencies between the petitions submitted, the inadequate identification of hours claimed on the computer printouts, and the overall lack of detailed analysis.” These calculations produced an award of $1,295,924. Finally, in order to compensate plaintiff for the time-value of money and to account for inflation, the court applied a multiplier of two. With rounding off, this procedure resulted in the award of $2.6 million.

II.

Although the district court never used the term “lodestar,” the court’s analysis paralleled the Third Circuit’s “lodestar” approach to determining reasonable attorneys’ fees. See Lindy Bros. Builders, Inc. of Philadelphia v. American Radiator & Standard Sanitary Corp., 540 F.2d 102, 109-18 (3d Cir.1976) (en banc) (“Lindy II”); Lindy Bros. Builders, Inc. of Philadelphia v. American Radiator & Standard Sanitary Corp., 487 F.2d 161, 167-69 (3d Cir.1973) (“Lindy /”). The “lodestar” approach involves two steps. First, the district court calculates a lodestar amount. To do this, the court determines the number of hours reasonably expended in the litigation. Of course the number of hours actually worked rarely equals the number of hours reasonably expended, so the court must disallow hours devoted to unrelated, unsuccessful claims and hours which the attorneys would not bill to their clients. See Copeland v. Marshall, 641 F.2d 880, 891-92 (D.C.Cir.1980) (en banc). Also excluded are hours for which the plaintiff provides inadequate documentation. See Hensley, 461 U.S. at 433, 103 S.Ct. at 1939. Multiplying the number of hours reasonably expended by the appropriate hourly rate or rates produces the lodestar amount — an initial, objective measure of the value of the attorneys’ time. In the present case, the district court calculated a lodestar of $1,295,924.

In the second step, the district court considers whether any special circumstances of the case justify adjusting the lodestar up or down. See Sangamo Construction Co., 657 F.2d at 862; see also Lynch v. City of Milwaukee, 747 F.2d 423, 426 (7th Cir.1984) (outlining twelve considerations and citing Hensley, 461 U.S. at 430 n. 3, 103 S.Ct. at 1937 n. 3 and Johnson v. Georgia Highway Express, Inc., 488 F.2d 714, 717-19 (5th Cir.1974)). For example, the court may consider whether the contingent nature- of success or the quality of representation merit an upward adjustment. See Cope land, 641 F.2d at 892-94; Lindy II, 540 F.2d at 117-18. Of course the court should not make any adjustment if the lodestar already reflects these factors. See Lindy 11, 540 F.2d at 117-18; see also Blum v. Stenson, 465 U.S. 886, 104 S.Ct. 1541, 1548-49, 79 L.Ed.2d 891 (1984) (no upward adjustment for novelty and complexity of issues since large number of hours claimed reflected that difficulty). In the present case, the district court adjusted the lodestar upward by a multiplier of two in order to compensate the plaintiff for inflation and for the time-value of money.

We begin with the issues related to calculating the lodestar, leaving the alleged errors in adjustments to the lodestar to Part III. Sealy did not appeal the lodestar calculation, but Ohio-Sealy raised a number of issues on its cross-appeal. Ohio-Sealy asserts that the district court abused its discretion (1) by disallowing twenty-five percent of the hours spent on equitable relief issues, (2) by using across-the-board hourly rates of $52 per hour for attorneys and $20 per hour for paralegals, (3) by relying on a Sealy exhibit that underestimated the number of hours claimed and rates charged, (4) by failing to compensate the plaintiff for time spent preparing the fee petitions, and (5) by reducing the basic monetary amount by fifteen percent for vagueness, inconsistencies, and inadequate identification of hours claimed. We will discuss each issue in turn.

A.

The district court disallowed 3017 attorney hours and 1082 paralegal hours as not reasonably expended on successful aspects of the litigation; these disallowed hours include twenty-five percent of all time spent on the equitable relief proceedings. Ohio-Sealy argues that this twenty-five percent disallowance contradicted the standard outlined by the Supreme Court in Hensley v. Eckerhart. We agree.

In Hensley, the Court established a two-part approach. First, the district court must eliminate hours spent on unrelated claims on which the plaintiff did not prevail. 461 U.S. at 434, 103 S.Ct. at 1939; cf. Spray-Rite Service Corp., 684 F.2d at 1251 (hours allowable if work bore on both successful and unsuccessful claims). That a plaintiff prevailed on one claim does not entitle him to recover attorneys’ fees for time spent on other, unrelated claims. See Hensley, 461 U.S. at 435, 103 S.Ct. at 1940; Spray-Rite Service Corp., 684 F.2d at 1251. Second, turning to the remaining hours, the district court must consider whether the plaintiff achieved “a level of success that makes the hours reasonably expended a satisfactory basis for making a fee award.” Hensley, 461 U.S. at 434, 103 S.Ct. at 1940. Where the plaintiff achieved only a limited success, the district court should award fees reasonably related to the results achieved; “the most critical factor,” the Court stated, “is the degree of success obtained.” Id. at 436, 103 S.Ct. at 1941.

In the present case, the district court concluded that Ohio-Sealy prevailed on seventy-five percent of the equitable issues and Sealy prevailed on the other twenty-five percent. (Memorandum Opinion and Order, at 16 (June 6, 1984)). The district court therefore disallowed twenty-five percent of the hours claimed by Ohio-Sealy. In Hensley, however, the Supreme Court rejected “a mathematical approach comparing the total number of issues in the case with those actually prevailed upon.” Hensley, 461 U.S. at 435-36 n. 11, 103 S.Ct. at 1940-41 n. 11 (quoting the district court in Hensley). The Court stated that such a ratio provided little assistance in considering all the relevant factors and determining what is a reasonable fee. Id.

The district court may have intended to eliminate the hours spent on unrelated claims on which Sealy prevailed. Ohio-Sealy clearly could not recover attorneys’ fees for such hours. See Hensley, 461 U.S. at 434-35, 103 S.Ct. at 1939-40; Copeland, 641 F.2d at 891-92 & n. 18. But the district court classified the hours by issues, not claims, and the court made no reference to whether the issues were related or unrelated. In addition, the court apparently made no attempt to determine the number of hours devoted to each equitable “issue.” Thus, even if the court meant that Ohio-Sealy did not prevail on twenty-five percent of its unrelated equitable claims, the district court’s approach did not consider whether those unsuccessful claims required more than or less than twenty-five percent of the total hours expended in the equitable relief litigation.

We can empathize with the trial judge who faced the chore of determining reasonable attorneys’ fees but received from the plaintiff voluminous documentation that failed to organize the data in a helpful manner. But although disallowing twenty-five percent of the hours claimed on the equitable issues may have seemed the fair thing to do, Hensley does not permit that approach. To the extent that the plaintiff’s evidence fails to provide the facts necessary for the Hensley approach, the district court may find that the plaintiff failed to meet the burden of establishing the number of compensable hours. See Hensley, 461 U.S. at 437, 103 S.Ct. at 1941. Furthermore, a district court may in its sound discretion apply a percentage reduction to account for a plaintiff’s limited success, but that discretion must be exercised in light of the considerations identified in Hensley. See id. at 436-37, 103 S.Ct. at 1941. Variations of the Hensley approach may suffice, but using a ratio of successful issues to total issues does not. The district court abused its discretion when it disallowed twenty-five percent of the hours because the plaintiff prevailed on only seventy-five percent of the equitable relief issues. Of course, on remand the district court may determine that a reduction of more than, less than, or exactly twenty-five percent is appropriate. See Illinois Welfare Rights Organization v. Miller, 723 F.2d 564, 569 (7th Cir.1983) (extent of plaintiff’s success is a question of fact).

B.

Ohio-Sealy also challenges the district court’s choice of reasonable hourly rates. The plaintiff contends that the district court abused its discretion by using “across-the-board rates of $52 per hour for all lawyers, including partners, and $20 per hour for paralegals.” The plaintiff claims these rates (1) were much lower than those awarded in comparable cases, (2) resulted from erroneous calculations, and (3) failed to consider individualized market-value rates.

Contrary to the plaintiff’s suggestion, the district court’s base figure reflected individual hourly rates. After the plaintiff failed to correlate specific hourly rates with hours claimed, Sealy filed an exhibit (Record 65, Exhibit Y) showing how many hours each of Ohio-Sealy’s attorneys and paralegals had billed at each hourly rate. The rates ranged from $23 to $135 per hour for attorneys and $11 to $44 per hour for paralegals. The exhibit concluded that Ohio-Sealy would have paid $1,685,-156.50 if it had paid for all the hours worked by its attorneys and paralegals. Since the exhibit matched each attorney’s hours with the rate charged for those hours, the base figure of $1,685,156.50 clearly reflected the individualized market rates for each attorney. See In re Fine Paper Antitrust Litigation, 751 F.2d 562, 583, 590-91 (3d Cir.1984). In fact, by using historical rates the calculations consider what rate each individual could command in the market at the time he or she performed the work. Thus the base figure of $1,685,-156.50 did not result from a $52 per hour across-the-board rate for attorneys and a $20 per hour rate for paralegals, and the district court’s method of obtaining a base figure was clearly permissible.

The district court did use the $52 per hour weighted average historical rate for attorneys and the $20 rate for paralegals, but only to correct the base figure for hours disallowed. The base figure of $1,685,156.50 reflected the value of some hours that Sealy argued were noncompensable. The district court agreed with some of Sealy’s arguments and disallowed 3017 attorney hours and 1082 paralegal hours. With the record before it, the district court could not determine which attorneys and paralegals worked the disallowed hours. The court consequently decided to adopt the defendant’s approach of using the weighted average historical rates. To obtain the rate for attorneys, the court took the base figure for attorneys (approximately $1.4 million of the $1,685,156.50) and divided by the total number of attorney hours. This yielded a weighted average historical hourly rate of $52 per hour. The court then subtracted the number of disallowed hours (3,017) from the number of hours claimed in the second supplemental fee petition (27,180) and multiplied the difference (24,163) by $52 per hour. This yielded the value of $1,256,476. This method reached approximately the same result as multiplying the number of disallowed hours (3,017) by $52 per hour and subtracting that figure from the attorney base figure. The district court used the same method to estimate the value of the compensable paralegal time.

The district court’s use of weighted average historical rates probably did not provide the true value of the disallowed hours, but the evidence in the record lacked the specificity to enable any method to compute the true value. The district court needed to determine the reasonable value of the hours it disallowed, and we think the court did not abuse its discretion by using a weighted average historical hourly rate for this purpose. See Copeland, 641 F.2d at 902 (approving the use of weighted historical average).

In addition to appealing the district court’s method in obtaining a base figure and determining the value of allowed hours, Ohio-Sealy asserts that the district court abused its discretion with respect to the numbers it used.

First, Ohio-Sealy claims that the Sealy exhibit (Record 65, Exhibit Y) contained inaccurate and incomplete information and that therefore the district court abused its discretion by basing its award on that exhibit. Although the plaintiff did not organize hours by attorney and appropriate historical hourly rate, the plaintiff did provide a list of all hours worked by each attorney and paralegal and each attorney’s and paralegal’s historical hourly rates. (Record 61, Schedules A, B, & C). Of course, the plaintiff bore the burden of establishing its compensable hours, see Spray-Rite Service Corp., 684 F.2d at 1249, and so the district court could to some extent rely on the defendant’s exhibit and underlying arithmetic when the plaintiff failed to furnish its own. But even though the district court did not need to plough through the voluminous documentation and totally recheck the accuracy of the tables in Sealy’s exhibit, the court had to ensure that the defendant’s tables and arithmetic relied on the same basic numbers that the court sought to use.

A cursory comparison of Ohio-Sealy’s schedules supplementing the fee petition (Record 61) with Sealy’s tables (Record 65) reveals that Sealy’s tables omit the more recent data. For example, the plaintiff’s schedules show that Mr. Brace charged $200 per hour after 1981, that Mr. North charged $120 per hour from January to September of 1982, and that Mr. O’Donnell charged $110 per hour from December, 1982 to July, 1983. (Record 61, Schedule A). In addition, the plaintiff’s schedules requested compensation for 9,430.75 hours of Mr. Brace’s time, 138.75 hours of Mr. North’s time, and 3,048.25 hours of Mr. O’Donnell’s time as an attorney. (Record 61, Schedule B). Sealy’s tables, which purport to show the total historical value for all hours claimed by Ohio-Sealy, show $135 per hour as the highest rate for Mr. Brace and $40 per hour as the highest rate for Mr. O’Donnell; the Sealy tables list Mr. Brace as working 9,271 hours and Mr. O’Donnell as working 1,695 hours. The defendant’s tables list neither an hourly rate nor hours worked for Mr. North, who represented the plaintiff in court on the attorneys’ fees issue. (Transcript of Proceedings, June 25, 1982, August 5, 1982, September 14, 1982).

This court may not reverse a district court’s finding of fact merely because we would have weighed the evidence differently than the district court. A district court’s findings, even when based on physical or documentary evidence, must stand unless clearly erroneous. See Fed.R. Civ.P. 52(a); Anderson v. City of Bessemer City, — U.S. -, 105 S.Ct. 1504, 1511-12, 84 L.Ed.2d 518 (1985). Nonetheless, a district court abuses its discretion when it bases a fee award on findings that are clearly erroneous. See Metlyn Realty Corp. v. Esmark, Inc., 763 F.2d 826, 831 (7th Cir.1985) (abuse of discretion if “no reasonable man could agree with the district court”); Lindy II, 540 F.2d at 115-16 (clearly erroneous finding of fact may require reversal). Although on the facts of this case, the district court did not abuse its discretion in using the weighted average historical rates to calculate the value of the allowable attorneys and paralegal hours, the district court’s adoption of Sealy’s base figure (hours times corresponding historical rate), without adjustment for the apparent errors in the Sealy tables, was clearly erroneous. The base figure corresponded to fewer hours than the district court wanted to compensate; if the district court wanted to obtain a weighted average historical rate for the 27,180 hours claimed in the second supplemental fee petition, the court should have used the base figure corresponding to those hours. Using Sealy’s base figure, which represented the value of only 25,710.50 hours, and then dividing by 27,180 hours caused the district court to underestimate both the weighted average historical hourly rate and the value of the allowed hours. We therefore hold that the district court abused its discretion by using a base figure that did not correspond to the number of hours the court used in its calculations.

Ohio-Sealy also argues that the district court failed to award fees for time spent preparing the fee petitions. In denying the plaintiffs motion for reconsideration, the district court stated that it had compensated the plaintiff for this time by basing the calculations on the larger number of hours requested in the second supplemental fee petition rather than the smaller number of hours claimed in the seventh supplemental fee petition. (Memorandum Opinion and Order, at 6 (October 1, 1984)). In fact, the district court had accepted the base figure (hours times appropriate historical hourly rate) provided in the Sealy exhibit. (Memorandum Opinion and Order, at 18-19 (June 6, 1984); Record 65). That base figure corresponded to 1,469.50 fewer attorney hours and 201 fewer paralegal hours than those listed in the second supplemental fee petition. The base figure also accounted for 1,098.8 fewer attorney hours but 25 fewer paralegal hours than the seventh supplemental fee petition. (Record 17). According to our own rough calculations, including all the hours of the second supplemental fee petition at the appropriate historical rates would increase the base figure by approximately $80,000. Since the base figure used by the district court accounted for fewer hours than those requested in either the second or seventh supplemental fee petition, the district court abused its discretion in ruling that the fee awards gave the plaintiff the benefit of additional hours and that these hours compensated the plaintiff for time its attorneys spent in the attorneys’ fees litigation.

C.

The district court concluded that, using the weighted average historical hourly rates, the total value of hours was $1,524,616. The court then reduced this amount by fifteen percent (to $1,295,924) because the court found the fee petitions vague, inconsistent, and lacking adequate identification of hours. Ohio-Sealy argues that the district court abused its discretion in making this reduction because the percentage reduction constituted an impermissible negative multiplier. The plaintiff also contends that the district court failed to specify which entries were vague, referred to an inconsistency that did not exist, and issued an erroneous order that required the plaintiff to reclassify the hours worked by issues rather than by claims. We hold that the district court did not abuse its discretion in making this reduction.

Ohio-Sealy asserts that the fifteen percent reduction constituted an impermissible negative multiplier. In Lynch, we reversed the district court’s use of a one-third negative multiplier, holding that the circumstances of that case did not justify such a penalty. 747 F.2d at 429-30. We stated that, “in all but the most unusual circumstances, any downward modification of the lodestar figure should be for one of the [twelve factors outlined in Johnson, 488 F.2d at 717-19] and should be expressed in a dollar amount.” Id. at 430. Lynch does not apply here, however, because in this case the district court used the fifteen percent reduction to obtain a lodestar rather than to apply a penalty after computing a lodestar. The lodestar refers to the product of the number of compensable hours times a reasonable hourly rate (or rates). In the present ease, the district court first subtracted the number of hours spent on unsuccessful claims and multiplied the remaining number of claimed hours by the weighted average historical hourly rate. But the district court also thought that the plaintiff’s documentation did not adequately establish all the remaining hours. The district court therefore reduced the value of the remaining hours — or, in effect, reduced the number of hours found compensable — by fifteen percent for the plaintiff’s failure to meet its burden of establishing that the hours claimed were compensable. Consequently, $1,295,924, and not $1,524,616, reflected the historical market value of compensable hours or, in other words, the lodestar. The fifteen percent reduction was used to compute a lodestar; it did not constitute an impermissible penalty that reduced the fee award to less than the value of the hours the plaintiff established as reasonably expended. On the facts of this case, the district court did not abuse its discretion by using a percentage rather than a dollar amount to correct for inadequately documented hours. See Lynch, 747 F.2d at 430 n. 7 (citing Copeland as example of when percentage reduction is appropriate).

Citing In re Fine Paper Antitrust Litigation, 751 F.2d 562 (3d Cir.1984), the plaintiff argues that a district court must identify allegedly “vague” entries and limit the reduction to the time covered by those entries. 751 F.2d at 595-96. In Fine Paper, the district court had analyzed each attorney’s time and disallowed some time with findings such as the following:

14.3 hours are supported by entries which are too vague to provide any basis for determining if the time spent was of value to the class. Many entries simply give the names of other attorneys and indicate that a conference or telephone call occurred.

In re Fine Paper Antitrust Litigation, 98 F.R.D. 48, 129 (E.D.Pa.1983), reversed and remanded, 751 F.2d 562 (3d Cir.1984). The Third Circuit held that this finding did not identify the disallowed hours and therefore remanded for the district court to identify the entries comprising the disallowed time. 751 F.2d at 596. By contrast, the District of Columbia Circuit held that a district court did not need to identify precisely the hours it disallowed: the district court could simply reduce the proposed fee award by a reasonable amount without performing an item-by-item accounting. See Copeland, 641 F.2d at 903. See also New York State Association for Retarded Children, Inc. v. Carey, 711 F.2d 1136, 1146 (2d Cir.1983) (endorsing percentage cuts as a practical way to trim fat from a fee application).

We think the Third Circuit’s approach is simply impractical in cases such as this one. The record in this case contains pages and pages of computer printouts describing how attorneys and paralegals spent their time — down to the quarter hour. In the district court, Sealy identified 978.25 hours of Mr. Brace’s time that Sealy thought was either unrelated to the litigation or had too vague an entry. These 978.25 hours came from 475 differing entries, some accounting for only fifteen or thirty minutes. Assuming that fifteen percent of the time was inadequately described, identifying each vague or undecipherable entry would take hours and hours of the court’s time and require an order nearly as voluminous as the evidence. For a case of this size, we agree with the District of Columbia Circuit that an item-by-item accounting would be neither practical nor desirable. See Copeland, 641 F.2d at 903.

In the present case the district court’s statement regarding vagueness is not an ideal statement of the reasons for the reduction. See Hensley, 461 U.S. at 437, 103 S.Ct. at 1941 (district court must “provide a concise but clear explanation of its reasons for the fee award”); see also Heiar v. Crawford County, Wisconsin, 746 F.2d 1190, 1203-04 (7th Cir.1984) (district court “must do more than eyeball the request and if it seems excessive cut it down by an arbitrary percentage”). Nonetheless, we find the reasons given adequate to permit appellate review. See Lynch, 747 F.2d at 427-28. Having reviewed the record, we cannot say that the district court abused its discretion in reducing the award for vagueness. See Hensley, 461 U.S. at 433, 103 S.Ct. at 1939 (if plaintiff fails to document hours adequately, court may reduce award accordingly).

Ohio-Sealy also argues that the inconsistencies cited by the district court do not exist. As an example of the inconsistencies in the plaintiff’s fee petition, the district court noted that the plaintiff’s sixth supplemental fee petition, which covered hours from July, 1970 to February, 1984, requested compensation for 1,743 fewer hours than the fifth supplemental fee petition, which covered hours from July, 1970 to May, 1983. (Memorandum Opinion and Order, at 19-20 (June 6, 1984)). Ohio-Sealy contends that no discrepancy existed because the plaintiff had informed the court that the plaintiff had voluntarily eliminated some of the hours previously listed. The plaintiff’s citations to the district court record support the plaintiff’s contention that it voluntarily eliminated some hours, but the record discloses that Ohio-Sealy conceded either 947.50 hours or 1,468 hours. (Record 56, at 12, 18, 24). Both of these numbers are less than the 1,743 hour difference noted by the district court, and, since the plaintiff requested compensation for additional hours worked between May, 1983 and February, 1984, the unexplained difference would be greater than 1,743 less 947.50 or 1,468, whichever is correct. The district court did not err in finding that the plaintiff’s fee petitions were inconsistent.

The plaintiff claims that most of the inexactitude resulted from an erroneous order of the district court. The district court criticized the plaintiff’s fee requests for referring to the number of hours as “more than,” “approximately,” “about,” and “perhaps.” (Memorandum Opinion and Order, at 9 (June 6, 1984)). We initially note that many of the hours cannot be easily categorized — not because the district court ordered them reclassified, but because the documentary evidence provides only vague or incomplete descriptions. Even if some of the inexactitude did result from an erroneous district court order, the vagueness of the descriptions, the inconsistencies between the petitions, and the plaintiff’s failure to provide detailed analysis provided adequate grounds for reducing the award. The issue of reasonable attorneys’ fees lies primarily within the sound discretion of the district court. In this case, the district court did not abuse that discretion in reducing the value of initially allowed hours by fifteen percent.

III.

Having reviewed the district court’s computation of a lodestar amount, we turn to the issues concerning the multiplier. Sealy contends that the district court abused its discretion by using a multiplier of two to compensate Ohio-Sealy for the time-value of money and for inflation. Ohio-Sealy argues that the district court properly accounted for interest and inflation but that the district court erred when it failed to discuss whether the lodestar should be adjusted upward for quality of representation and for risk.

A.

We start with the quality issue. The plaintiff bore the burden of proving that the hourly rate did not accurately reflect the quality of the attorneys’ work. See Blum, 104 S.Ct. at 1548-49; Copeland, 641 F.2d at 893-94; see also In re Illinois Congressional Districts Reapportionment Cases, 704 F.2d 380, 384 (7th Cir. 1983). As the Supreme Court recently stated in Blum:

The “quality of representation,” however, generally is reflected in the reasonable hourly rate. It, therefore, may justify an upward adjustment only in the rare case where the fee applicant offers specific evidence to show that the quality of service rendered was superior to that one reasonably should expect in light of the hourly rates charged and that the success was “exceptional.”

104 S.Ct. at 1549. In the present case, the plaintiff hired one of the largest firms in the country, and has offered no evidence that that firm charged less than what the attorneys’ time was worth. Ohio-Sealy may have received top quality work, but it paid top dollar for that work. Absent any specific evidence that the hourly rate did not reflect the quality of the plaintiff’s attorneys’ work, the district court did not abuse its discretion in failing to discuss the quality issue. See Blum, 104 S.Ct. at 1549; Lindy 11, 540 F.2d at 118 (“heavy burden” of proving quality adjustment is on the moving party).

Ohio-Sealy argues that it offered no specific evidence because the district court denied the plaintiff’s request to discover the number of hours spent by Sealy’s attorneys defending this lawsuit. The plaintiff asserts that this information would provide the best evidence that OhioSealy’s attorneys worked more efficiently than Sealy’s attorneys and that Ohio-Sealy is therefore entitled to an upward adjustment for quality. Proof that the defendant’s attorneys worked more hours than the plaintiff’s attorneys does not, however, mean that the plaintiff’s attorneys worked more efficiently. We would normally expect a defendant to invest more in defending an antitrust suit than a plaintiff would invest in prosecuting it. After all, if a defendant loses, it must pay treble damages, the cost of defending, and the plaintiff’s reasonable costs of bringing the suit; if the plaintiff loses, it is out only costs and whatever fees it paid its attorneys. Even apart from potential loss, the task of defending a civil case may require more work than the task of prosecuting. See Samuel v. University of Pittsburgh, 80 F.R.D. 293, 294-95 (W.D.Pa.1978). The number of hours spent defending the case may therefore have little relevance to the number of hours reasonably expended by the plaintiff’s counsel. See Mirabal v. General Motors Acceptance Corp., 576 F.2d 729, 731 (7th Cir.), cert. denied, 439 U.S. 1039, 99 S.Ct. 642, 58 L.Ed.2d 699 (1978); Samuels, 80 F.R.D. at 294. But see Fine Paper Antitrust Litigation, 751 F.2d at 589 (quality multiplier might be appropriate if attorney achieved result “with unusual efficiency, and with little expenditure of attorney time and expense”). Without suggesting that the court would have erred by compelling discovery, we hold that the district court did not abuse its discretion by denying the plaintiff's motion to compel discovery of the hours worked by Sealy’s attorneys. See Johnson v. University College of the University of Alabama in Birmingham, 706 F.2d 1205, 1208 (11th Cir.), cert. denied, 464 U.S. 994, 104 S.Ct. 489, 78 L.Ed.2d 684 (1983).

B.

Courts have frequently stated that district courts may add a bonus to the lodestar to compensate for the contingent nature of success. See Copeland, 641 F.2d at 892-93; Lindy II, 540 F.2d at 117. This category of adjustments to the lodestar includes compensation for the risks assumed in developing the case and for the time-value of money. See Lindy II, 540 F.2d at 117. The plaintiff argues that the district court abused its discretion by not considering the risk factor but that the court properly adjusted the lodestar for inflation and for the time-value of money. The defendant argues that when attorneys work on an hourly rather than contingency basis, the plaintiff cannot obtain a multiplier for the contingent nature of success. We think the defendant is correct with respect to bonuses for the contingent nature of success. Nevertheless, we believe the fee award should compensate the plaintiff for inflation, although not as compensation for the contingent nature of success.

The reasons for enhancing a lodestar amount for the contingent nature of success apply to lawyers, not their clients. In Copeland, the District of Columbia Circuit stated that the “fundamental purpose of the fee award is to compensate the attorney for his efforts.” 641 F.2d at 891. “It is important to recognize,” that court said, “that the contingency adjustment is designed solely to compensate for the possibility at the outset that the litigation would be unsuccessful and that no fee would be obtained.” Id. at 893. The contingency factor discussed in applying a multiplier to a lodestar is not, however, the type of contingency fee typical in tort eases. See id. at 893; Blum v. Stenson, 104 S.Ct. at 1551 n. 1 (Brennan, J., concurring). The factor for the contingent nature of success reflects a refinement in estimating the market value of an attorney’s services. The hourly rates used to compute the lodestar are typically the rates lawyers charge clients who pay on a regular basis — win or lose. See Hensley, 461 U.S. at 448, 103 S.Ct. at 1947 (Brennan, J., concurring); Copeland, 641 F.2d at 893. By using a multiplier, courts attempt, in effect, to estimate the hourly rate which — at the start of litigation — a lawyer would agree to use if he and the client agreed that the client would pay the bill at the end of the lawsuit and only if they won. See In re Fine Paper Antitrust Litigation, 751 F.2d at 603 (Becker, J., concurring) (contingent factor may change if an initial settlement reduces the risk associated with the remaining litigation). Thus the upward adjustment or multiplier compensates the lawyers for the risk of never being paid and the time-value of money. See, e.g., Chrapliwy v. Uniroyal, Inc., 670 F.2d 760, 770 (7th Cir.1982) (over course of seven-year litigation, attorneys invested 11,000 hours with no compensation), cert. denied, 461 U.S. 956, 103 S.Ct. 2428, 77 L.Ed.2d 1315 (1983).

In the present case, Ohio-Sealy paid its lawyers on a regular hourly basis. The lawyers neither risked noncompensation nor endured a delay before payment. Therefore, in terms of compensating the lawyers, the court had no reason to adjust the lodestar upward for a risk of no compensation or a delay in receipt of payment.

Ohio-Sealy argues that, by paying its lawyers on an hourly basis, it accepted the risk of no compensation and the loss of the time-value of money. Since the attorneys’ fee award belongs to the plaintiff, there exists no reason, the plaintiff asserts, why the district court cannot use a multiplier to compensate the plaintiff for these factors. We disagree.

Ohio-Sealy argues that we should not distinguish between hourly and contingency fee arrangements. Language in Illinois v. Sangamo Construction Co., 657 F.2d 855 (7th Cir.1981), provides the strongest support for this argument. In that case we stated that “[t]he amount plaintiff actually pays his attorney is irrelevant, since the determination of what is a ‘reasonable’ fee is to be made without reference to any prior agreement between the parties.” 657 F.2d at 861; see also Farmington Dowel Products Co. v. Forster Mfg. Co., 421 F.2d 61, 86-90 (1st Cir.1969). For two reasons, we think the quoted language from Sangamo Construction Co. does not apply here.

First, the compensation agreement between the client and attorney in Sangamo Construction was irrelevant not because a private attorney’s rate had no probative value but because the salaries of the assistant attorneys general provided no probative evidence of the prevailing market rate. See also Blum, 104 S.Ct. at 1547 (legal aid lawyer). When a plaintiff pays an attorney in private practice on an hourly basis, the hourly rate is clearly relevant in determining the prevailing market rate for such services. See Blum, 104 S.Ct. at 1547 n. 11.

Second, the rationale for awarding a multiplier for the contingent nature of success violates the “rule” of Sangamo Construction. If the determination of a “reasonable fee” is to be made without reference to the agreement between the parties, courts have no reason to discuss what type of fee arrangement the plaintiff had with its attorneys. After all, as the plaintiff points out, the fee award technically belongs to the plaintiff and not to the attorneys. See Sangamo Construction, 657 F.2d at 861. Yet, far from ignoring the fee arrangements between an antitrust plaintiff and his attorneys, the courts applying multipliers for the contingent nature of success have emphasized the contingent nature of the fee agreement. Thus cases cite such facts as counsel risked more than 6,100 hours of work without guarantee of remuneration, incurred $60,000 in litigation expenses, and entered the litigation knowing that they would not receive any payment for five or more years. See AAMCO Automatic Transmissions, Inc. v. Tayloe, 82 F.R.D. 405, 415 (E.D.Pa.1979). Thus the upward adjustment or multiplier is based on a factor which, if Sangamo Construction were read broadly, is irrelevant.

We do not mean to imply that a multiplier for the contingent nature of success is inappropriate when lawyers bear the risk of nonpayment and the delay in payment. But looking to the contingent nature of success borne by the attorneys is inconsistent with the statement that courts must ignore the fee agreement. Courts should probably ignore the percentage chosen as the contingency rate or an unreasonably high or low hourly rate, but courts may consider — and have considered — the fact that the attorney worked on a contingency or an hourly basis. See Blum, 104 S.Ct. at 1551 (Brennan, J., concurring); Waters v. Wisconsin Steel Works of International Harvester Co., 502 F.2d 1309, 1322 (7th Cir.1974) (listing “[wjhether the fee is fixed or contingent” as a factor to be considered when adjusting the amount determined by “hours spent times billing rate”), cert. denied, 425 U.S. 997, 96 S.Ct. 2214, 48 L.Ed.2d 823 (1976); see also Sangamo Construction Co., 657 F.2d at 862 & n. 6 (following Waters).

We must now decide whether the policies underlying section 4 of the Clayton Act support Ohio-Sealy’s contention that it should receive an upward adjustment since it bore the risks in this case. In Sangamo Construction, we outlined three basic purposes of the fee award of section 4:

1) to encourage private enforcement of the antitrust laws, 2) to insure that the cost of doing so does not diminish the treble damages award, and 3) to deter violations of the antitrust laws by requiring the “payment of that fee by a losing defendant as part of his penalty for having violated the antitrust laws.”

Sangamo Construction Co., 657 F.2d at 859-60 (quoting Farmington Dowel, 421 F.2d at 90). An award of fees, without an upward adjustment for the contingent nature of success fulfills these purposes. True, allowing the plaintiff to recover a bonus for the contingent nature of success would increase the plaintiff’s incentive and the defendant’s penalty. On the other hand, the attorneys’ fees award should not provide a windfall for the plaintiff. See Hensley, 461 U.S. at 430 n. 4, 103 S.Ct. at 1938 n. 4; New York State Association for Retarded Children, 711 F.2d at 1152-53. But see Sangamo Construction, 657 F.2d at 861-62 (windfall allowed when caused by plaintiff not paying prevailing market rate). The treble damages provide the primary inducement for private parties to bring antitrust actions; the section 4 provision for awarding attorneys’ fees encourages plaintiffs to bring actions because it guarantees that a successful plaintiff will not find his treble damage award unduly diminished by the costs of litigation. See Twin City Sportservice, Inc. v. Charles O. Finley & Co., 676 F.2d 1291, 1312 (9th Cir.), cert. denied, 459 U.S. 1009, 103 S.Ct. 364, 74 L.Ed.2d 400 (1982); Perkins v. Standard Oil Co. of California, 474 F.2d 549, 553 (9th Cir.), cert. denied, 412 U.S. 940, 93 S.Ct. 2778, 37 L.Ed.2d 400 (1973), modified on other grounds, 487 F.2d 672 (9th Cir.1973). When a plaintiff paid his attorney on an hourly basis, the fee award that compensates the plaintiff for the hours reasonably worked by the attorney adequately protects the treble damages award.

In addition, the principal purpose of the bonus or upward adjustment for the contingent nature of success is not one of the three purposes listed above. Instead, the bonus, both in antitrust and civil rights eases, provides an inducement for lawyers to accept meritorious cases that might otherwise go unheard. See Blum, 104 S.Ct. at 1551 (Brennan, J., concurring); In re Illinois Congressional Districts Reapportionment Cases, 704 F.2d at 384; see also New York State Association for Retarded Children, 711 F.2d at 1154 (bonus for risk of failure appropriate only to entice private firms to take case, no bonus for non-profit organizations that exist to bring such claims). For the plaintiff, the treble damages provide the inducement to accept the risk of litigation — a risk the plaintiff takes in every case, although admittedly a less costly risk when his attorneys work on a contingency basis. See Hensley, 461 U.S. at 448-49, 103 S.Ct. at 1947 (Brennan, J., concurring) (“risk of nonrecovery usually borne by clients in cases where lawyers are paid an hourly rate”). Furthermore, plaintiffs may collect interest on attorneys’ fees or costs only from the date that the award is entered. See Perkins v. Standard Oil Co. of California, 487 F.2d 672, 675 (9th Cir.1973); Independence Tube Corp. v. Copperweld Corp., 543 F.Supp. 706, 716 (N.D.Ill.1982); cf. Harris v. Chicago Great Western Ry., 197 F.2d 829, 836 (7th Cir.1952) (interest awarded only after fees obligation was “authoritatively defined”). But see Copper Liquor, Inc. v. Adolph Coors Co., 701 F.2d 542, 545 (5th Cir.1983) (en banc) (interest begins to run on date of judgment if plaintiff unconditionally entitled to fees). It would be inconsistent to permit the district court to do indirectly with a multiplier what it cannot do directly with prejudgment interest. We therefore hold that a district court may not make an upward adjustment for the “contingent nature of success” when the plaintiff compensated his counsel at hourly rates and as the litigation progressed.

C.

The district court could, however, adjust the lodestar to compensate for inflation. An upward adjustment for inflation is appropriate not because of the contingent nature of success but because an attorneys’ fees award should compensate the plaintiff for reasonable fees paid. In applying a multiplier for inflation, the district court sought to award Ohio-Sealy a dollar amount with the same purchasing power as the dollars Ohio-Sealy paid its attorneys. If a successful antitrust plaintiff’s attorneys billed the plaintiff for a reasonable number of hours at the prevailing market rates, a section 4 fee award should compensate the plaintiff for this expense. Awarding the nominal amount of the attorneys fees will not fully compensate the plaintiff if the litigation lasted a number of years. Due to inflation, today a dollar has less purchasing power than the dollars OhioSealy paid its lawyers in 1971. Failing to correct for inflation would give the defendant a motive to prolong the fee issue as long as possible, and antitrust cases last long enough as it is. The district court therefore did not abuse its discretion in attempting to adjust the lodestar for inflation; the district court did abuse its discretion, however, in choosing a multiplier of two.

Ohio-Sealy correctly points out that in Chrapliwy v. Uniroyal, Inc., 670 F.2d at 764 n. 6, this court suggested that a district court compensate for delay by a computation of interest, a percentage allowance for inflation, or a similar allowance in choosing a “so-called multiplier.” By that comment, we did not mean to imply that any of the three could be used in every case. Nor did we mean to imply that these provide the exclusive means of adjusting the lodestar. Rather, in exercising its discretion, the district court can choose the method that it reasonably believes is best suited for the case.

In the present case, the plaintiff is not entitled to an award of interest, so the first suggested method is inapplicable. To correct for inflation, using current rather than historical hourly rates might prove adequate if the litigation lasted only a few years. See New York State Association for Retarded Children, 711 F.2d at 1152. When a case lingers on for a long time, however, using current hourly rates may produce a windfall for the plaintiff since changes in hourly rates reflect not only inflation but also an attorney’s increased experience and skill. See id.; Locklin v. Day-Glo Color Corp., 378 F.Supp. 423, 427 (N.D.Ill.1974); see also Hensley, 461 U.S. at 430 n. 4, 103 S.Ct. at 1938 n. 4 (fee awards not intended to produce windfalls); but see In re Amyicillin Antitrust Litigation, 81 F.R.D. 395, 402 (D.D.C.1978) (using current rates even though litigation lasted eight years). This case has now entered its fifteenth year, so the district court did not abuse its discretion in refusing to use current hourly rates in computing the lodestar amount. Cf. New York State Association for Retarded Children, 711 F.2d at 1153 (dividing litigation into two time periods and giving different maximum rate for each); AAMCO Automatic Transmissions, 82 F.R.D. at 412, 415-16 (using historical rates to compute lodestar and then adding a specific amount for contingent nature of success).

Of course a multiplier also provides less than a perfect tool. The problem with a multiplier is that it increases the entire lodestar by the same amount, even though the fees paid in 1970 have witnessed much more inflation than those paid in 1980. When the attorneys provided the services over a long period of time, a multiplier is appropriate only if, although it corrects the fees of earlier years too little and the fees of later years too much, the multiplier results in an upward adjustment that approximates the total effect of inflation. In the present case, the district court justified its multiplier of two on the ground that it yielded about the same result as using current rates, an approach which the court had previously rejected as likely to result in a windfall for plaintiffs. (Memorandum Opinion and Order, at 7, 20 (June 6, 1984)). The court also reasoned that it had to “apply a visceral reaction to the entire thing to come up with what it can honestly believe to be a fair fee.” (Memorandum Opinion and Order, at 5 (October 1, 1984)). Although the district court undoubtedly has the best feel for what fee is fair and just, we think the court abused its discretion by not using a more analytical approach in choosing the multiplier. See, e.g., Chrapliwy v. Uniroyal, Inc., 509 F.Supp. 442, 457-58 (N.D.Ind.1981) (justifying use of current rates with increase in Consumer Price Index and contingent nature of case), aff'd in part and rev’d in part on other grounds, 670 F.2d 760 (7th Cir.1982), cert. denied, 461 U.S. 956, 103 S.Ct. 2428, 77 L.Ed.2d 1315 (1983).

We should note, however, that the reason for the district court’s inability to correct more precisely for inflation was the plaintiff’s failure to submit evidence of actual fees paid to its attorneys. The district judge repeatedly noted his need for this information. Had the plaintiff submitted evidence of actual fees paid, the district court could have easily calculated a lodestar that corrected for inflation, with no need for a multiplier. But the district court lacked this information, and on remand will have to determine whether the record permits a more precise correction for inflation.

IV.

We affirm the district court’s opinion with respect to the use of a weighted average historical hourly rate to determine the value of the allowable hours. We also affirm the court’s decision to reduce the base figure by fifteen percent due to vague entries and inconsistencies in the plaintiff’s fee petitions. We reverse the twenty-five percent reduction of hours devoted to equitable relief issues and the court’s use of a base figure that did not correspond to the number of hours in the fee petition relied on by the court.

With respect to adjustments to the lodestar amount, we hold that Ohio-Sealy cannot recover an upward adjustment for the contingent nature of success because it paid its attorneys on an hourly basis. We also hold that the district court did not abuse its discretion to the extent that it attempted to compensate the plaintiff for inflation, but the court failed to provide sufficient justification for the multiplier it chose.

In holding that the district court abused its discretion in some aspects of this fee contest, we do not do so critically. There is a practical limit to what a busy trial judge may be expected to do with the massive fee detail engendered by protracted litigation. As Justice Powell wrote in Hensley “[a] request for attorney’s fees should not result in a second major litigation.” 461 U.S. at 437, 103 S.Ct. at 1941. Counsel who seek fees have the duty to justify the fees with reasonable, organized, and understandable data so that the trial judge may fairly and expeditiously resolve the fee issue. Counsel who oppose the fees have a similar responsibility to state objections with particularity and clarity. Miscellaneous fee data cannot just be dumped on the bench for the judge to sort through and resolve. We believe that Judge Parsons on remand, assisted by the guidance we have tried to give with this opinion, will set as fair a fee as is judicially possible. Even though we do not reach the merits of the issue whether an evidentiary hearing was needed in this case, see note 13, Judge Parsons, if he deems it helpful, may enlist the help of the magistrate, see 28 U.S.C. § 636, or a special master, see Fed.R.Civ.P. 53, or undertake it himself with an evidentiary hearing. We regret the necessity of remand requiring the expenditure of more judicial time by the trial judge in the tiresome task of trying to unravel and resolve this complex fee setting problem, and therefore urge the parties in good faith to endeavor to settle their attorneys’ fees among themselves. Circuit Rule 18 shall not apply on remand.

Affirmed In Part, Reversed In Part, And Remanded. 
      
      . Ohio-Sealy filed eight appendices with its initial brief. These appendices consisted of tables of numbers of hours, billing rates, and fee awards based on differing interest rates. Each appendix also listed its sources; for example, Appendix C lists 34 sources for the information listed in the tables. Sealy moved to strike these appendices on the ground that none of the tables and charts in the appendices was a part of the trial court record. Ohio-Sealy responded that the appendices simply reflect summaries of the voluminous evidence in the district court record, interest rates published in the Federal Reserve Bulletin, and mathematics. Sealy argued that the numbers of hours listed in the appendices are not supported by or are inconsistent with the record; Sealy identified a number of alleged discrepancies.
      Evidence not presented to the trial court may not be offered on appeal. See Rebuck v. Vogel, 713 F.2d 484, 486 (8th Cir.1983); see also Fed.R. App.P. 10(a) (record on appeal consists of "original papers and exhibits filed in the district court, the transcript of proceedings, if any, and a certified copy of the docket entries prepared by the clerk of the district court”). The plaintiff argues that summaries of voluminous materials are simply tools to aid this court in understanding the record, but the cases the plaintiff cites lend no support to this proposition. Those cases refer to summaries admitted by the trial court, not an appellate court. As the Third Circuit stated, "[sjummaries of voluminous business records are admissible in evidence where the records are already in evidence, permitting independent verification of the summaries." Meister v. Commissioner, 504 F.2d 505, 513 (3d Cir.1974), cert. denied, 421 U.S. 964, 95 S.Ct. 1951, 44 L.Ed.2d 450 (1975). If Ohio-Sealy thought these summaries were so helpful and important, it should have submitted them to the district court. Then the defendant could have contested those portions of the tables that it claims are inconsistent with the record, and the district court could have made a factual finding. The motion to strike is granted. See Cox v. Northwest Airlines, Inc., 379 F.2d 893, 896-97 (7th Cir.1967), cert. denied, 389 U.S. 1044, 88 S.Ct. 788, 19 L.Ed.2d 836 (1968).
     
      
      . These average rates are referred to as weighted average historical hourly rates because the value for total fees based on historical rates reflects not only the various hourly rates but also how many hours were worked at each rate. Using an average hourly rate without considering the number of hours worked at each rate could overestimate the weighted average if attorneys worked most of the hours at lower rates or underestimate the weighted average if most of the hours were worked at higher rates.
     
      
      . The division of issues between those relevant to computing a lodestar and those relevant to adjustments is not always consistent. For example, if a court decides to use current hourly rates to compensate the attorneys for inflation and the time-value of money, the lodestar reflects this adjustment and no further adjustment is appropriate. See, e.g., Chrapliwy v. Uniroyal, Inc., 670 F.2d 760, 764 (7th Cir.1982); Copeland, 641 F.2d at 893 n. 23. The district court can make an adjustment in the process of computing a lodestar or after computing a lodestar, so long as the court provides an explanation for each adjustment and does not adjust for the same factor twice. See Hensley, 461 U.S. at 437, 103 S.Ct. at 1941 (district court should provide concise but clear explanation of fee award). The district court is in the best position to determine what fees are reasonable, and the court does not abuse its discretion by modifying the lodestar or other fee setting approach into a method more convenient on the facts of a particular case.
     
      
      . Technically, this second consideration falls within the adjustment step of the lodestar approach to attorneys’ fees awards. The district court could weigh this consideration in computing the lodestar, however, as long as it made no subsequent adjustment for the results obtained. See supra note 3. See generally K. Ripple, Constitutional Litigation 365 (1984) (outlining the Hensley approach).
     
      
      . The defendant argues that the district court followed the Supreme Court’s directive to “focus on the significance of the overall relief obtained by the plaintiff in relation to the hours reasonably expended on the litigation." Hensley, 461 U.S. at 435, 103 S.Ct. at 1940. Sealy contends that Ohio-Sealy did not prevail on the most important issues with respect to equitable relief and that therefore the district court could have found that the plaintiff’s success was far less than the seventy-five percent allowed. We offer no opinion as to the correctness of the defendant’s assertion because the district court’s order clearly reveals that the court used a ratio of “issues prevailed on” to “total issues” to determine the number of allowable hours. See id. at 437, 103 S.Ct. at 1941 (important for the district court to provide concise but clear explanation of reasons for fee award). Whether the issues Ohio-Sealy lost were the most important remains a factual matter for the district court to determine on remand.
     
      
      . For example, the table reflecting the charges for Ohio-Sealy’s lead counsel read as follows:
      Date Rate Hours Total
      04/71-04/73 50.00 3,003.00 $ 150,150.00
      05/73-01/74 65.00 866.50 56,322.50
      
        Date Rate Hours Total
      02/74-11/74 70.00 1.343.50 $ 94,045.00
      12/74-03/76 75.00 1.621.00 121,575.00
      04/76-06/77 80.00 1.137.50 91,000.00
      07/77-01/78 85.00 314.75 26,753.75
      02/78-06/78 90.00 ■‘261.25 23,512.50
      07/78-12/78 100.00 66.75 6,675.00
      01/79-05/79 105.00 93.75 9,843.75
      06/79-02/80 120.00 171.50 20,580.00
      03/80-07/80 125.00 84.50 10,562.50
      08/80-02/81 128.00 135.75 17,376.00
      03/17 /81 135.00 171.25 23,118.75
      9.271.00 $ 651,514.75
      Record 65, Exhibit Y.
     
      
      . Ohio-Sealy never submitted evidence on what it actually paid its lawyers; it only provided information on hours worked and hourly rates. Thus the plaintiffs fee request failed to consider the attorneys' billing practice, an important consideration in awarding attorneys’ fees. See Hensley, 461 U.S. at 434, 103 S.Ct. at 1939 (hours not billed to one’s client are not properly billed to an adversary under a fee-shifting statute). See infra note 18.
     
      
      . Since the plaintiff was represented in most of this litigation by one of the largest, and presumably more expensive, law firms in the country, the plaintiff is hard-pressed to complain that, at the time worked, the hourly rates fell below the prevailing market rate. See Blum v. Stenson, 465 U.S. 886, 104 S.Ct. 1541, 1547 n. 11, 79 L.Ed.2d 891 (1984).
     
      
      . The result is only approximately the same because the district court rounded off the average rate to $52 per hour. Multiplying the number of disallowed hours by $52 and subtracting would yield $1,243,116, a value lower and, consequently, less beneficial to the plaintiff.
     
      
      . Mr. O’Donnell started working on this case as a paralegal but has since become an attorney.
     
      
      . Some of the differences in hours worked could, of course, result from the plaintiff and defendant referring to different fee petitions. The failure to include higher rates probably resulted from Sealy's exclusion of all hours spent on the fee petitions, although the district court held that its calculations (based on the Sealy exhibit) compensated the plaintiff for these additional hours. Even with these possible explanations, however, the Sealy tables referred to fewer hours than the court intended to compensate. See pages 14-15.
     
      
      . Assuming for the sake of example that the correct average historical rates for attorneys and paralegals are $54.34 and $20, the values listed in Sealy’s tables (Record 65, Exhibit X), using the numbers from the second supplemental fee petition would increase the base figure by (1,469.50 X $54.34) + (201 X $20) = $83,-873.
     
      
      . The plaintiff also argues in its closing brief on the cross-appeal that the district court erred by not holding an evidentiary hearing on the vague entries. We do not address the merits of this argument because, by failing to raise this issue in its opening brief on the cross-appeal, the plaintiff waived the issue. See Publishers Resource, Inc. v. Walker-Davis Publications, Inc., 762 F.2d 557, 560 (7th Cir.1985); Cannon v. Teamsters & Chauffeurs Union, Local 627, 657 F.2d 173, 177-78 (7th Cir.1981).
     
      
      . The following were included in the defendant’s list of allegedly indecipherable entries or unrelated time:
      
        Date Hours Description
      12/08/80 1.50 LTR TO SHAREHOLDERS
      12/17/80 1.00 STAFF CNF CNF LBG PHN CNF REVIEW DRAFTS RESEARCH CORRESP MISC
      12/24/80 .25 CNFS, PHN CNFS & COR-RESP
      12/29/80 1.00 CORRESP, PHN CNFS, CNFS
      12/30/80 .50 CORRESP
      01/07/81 .25 MISC
      (Record 52, Exhibit 10).
     
      
      . In the conclusion of Ohio-Sealy’s Reply Regarding Attorneys’ Fees, the plaintiff states that the Reply reduces the total number of disputed hours by 1,468. (Record 56, at 24). The body of the Reply identifies only 947.50 hours that the plaintiff eliminated. (Record 56, at 12, 18).
     
      
      . Similarly, when an antitrust plaintiff seeks injunctive relief, the plaintiff knows that if he is successful the defendant will pay the reasonable costs and fees incurred by the plaintiff in obtaining the injunction. Cf. Copper Liquor, Inc. v. Adolph Coors Co., 624 F.2d 575 at 584 (5th Cir.1980) (public policy suggests that financial burden of correcting wrongdoing should be removed from shoulders of plaintiff).
     
      
      . The market interest rate reflects both the real interest rate and anticipated inflation. See generally P. Samuelson, Economics 272, 608-09 (10th ed. 1976). Therefore when awarding fees for attorneys who worked on a contingency basis, the interest rate may provide a useful tool for correcting for the contingent nature of success. The interest rate approach is not appropriate here since the plaintiff paid its lawyers on an hourly basis and therefore the plaintiff is entitled to a correction for inflation but not for a return on its fees as an investment.
     
      
      . Statements of annual fees paid by Ohio-Sealy to its lawyers in 1971 would reflect not only the then-prevailing market rates but also the lawyers’ billing judgment. See Hensley, 461 U.S. at 434, 103 S.Ct. at 1939 (hours not properly billed to a client are not properly billed to an adversary). After the district court reduced the actual fees paid by the value of noncompensable hours billed and for other appropriate factors, the court could correct for the amount of inflation since 1971 and obtain the present value of the 1971 fees. By proceeding similarly with the actual fees of other years, the lodestar would reflect the present value of the fees actually paid (corrected for noncompensable hours) from 1970 to 1984.
     