JOHNSON, Circuit Judge:
I. INTRODUCTION
This is an appeal and cross-appeal from a judgment and award of damages and in-junctive relief in an antitrust case brought under Section 1 of the Sherman Act. Plaintiff Tic-X-Press (TXP), a ticket-selling service located in Atlanta, Georgia, brought suit against the Atlanta Coliseum, Inc. (ACI), the Omni Promotions Company of Georgia (TOPCOG), the Omni Promotions Company, Limited (TOPCOL), and S.E.A. T. S., Inc. (SEATS). TXP’s complaint alleged that the defendants violated the Sherman Act’s prohibition against anticompeti-tive tying arrangements by conditioning the lease of the Omni Coliseum upon the use of SEATS, a ticket-selling agency affiliated with ACI, TOPCOL and TOPCOG. The district judge found that the defendants had violated the antitrust laws and awarded the plaintiff treble damages and injunctive relief as well as attorney’s fees. ACI, TOPCOL, TOPCOG and SEATS appeal the district court’s finding of antitrust liability and TXP cross-appeals both the damages award and the injunctive relief ordered by the district court. Both parties appeal the award of attorney’s fees. We reject the arguments raised on all of these issues and affirm the district court.
II. FACTS AND PRIOR PROCEEDINGS
TXP filed suit against the defendants/appellants/eross-appellees (hereinafter “appellants”) in federal district court on September 15, 1982, alleging violations of Sections 1 and 2 of the Sherman Act.1 15 U. S.C.A. §§ 1 & 2. Following a bench trial on the Section 1 claim, the Honorable Charles A. Moye entered the findings of fact and conclusions of law summarized below.
The Omni Coliseum is an enclosed facility in the City of Atlanta used for sporting events, musical concerts, and various other events. The Omni is the only arena in the Atlanta area with seating capacity adequate to accommodate in excess of 16,000 people, and the only enclosed arena with capacity to seat more than 4,000 people. There are other facilities in the Atlanta area for the production of concerts, but all are smaller or are not enclosed.2 The district court concluded that the Omni’s size and configuration make it a unique facility with a substantial economic advantage for the presentation of concerts where the audience attendance is expected to range between 4,000-16,000.
Pursuant to a series of agreements with the City of Atlanta and Fulton County Recreational Authority, the governmental body which owns the Omni, ACI and TOP-COL3 have the exclusive right to control the use and rental of the Omni. SEATS is a computerized ticketing service in the business of selling tickets for events at various facilities in the Atlanta area. ACI, TOPCOL, and SEATS are under common ownership and management and essentially function as a single entity.
ACI and TOPCOL frequently rent the Omni to promoters seeking to stage various musical concerts and other events in the Atlanta area.4 In negotiating with outside promoters for the use of the Omni, TOPCOL uses a standard form contract called the “Producer’s Agreement.” Paragraph 23 of the Agreement provides in
its rights regarding the Omni to TOPCOG on February 1, 1980, and TOPCOG assigned those same rights to TOPCOL in December 1986. Both TOPCO and TOPCOG were subsequently dissolved. For simplicity, we will refer to the entity which successively performed the functions of what is now TOPCOL as "TOPCOL" throughout this opinion. [1412]*1412pertinent part that “[a]ll ticket sales relating to the PRODUCER’S [i.e. the outside promoter’s] use of the Premises under this Agreement shall be made by PROMOTIONS’ [i.e. TOPCOL’s] box office or at other ticket agencies approved by PROMOTIONS...” Although TOPCOL technically does not have a box office (ACI does), there was no real dispute that the phrase “PROMOTIONS’ box office” referred to SEATS. Some of the agreements also had typed-in language providing that promoters were required to pay all fees and expenses immediately following the show, “including rent [and] a 3.5% ticket charge.” The 3.5% ticket charge represented the amount due SEATS for providing the ticketing services for the event. Promoters contracting to use the Omni never signed a separate contract or engaged in separate negotiation with SEATS.
The district court determined that Paragraph 23 of the “Producer’s Agreement” gives promoters the right to select a ticket agency approved by the appellants. The district court also determined that the appellants had legitimate business interests in approving the ticket agency for Omni events, such as the safety of ticket sale proceeds, the adequacy of the ticket distribution network, and the financial integrity of the agency. The district court found, however, that the appellants had never established any written specifications or procedures for approving other ticketing services.
TXP is a ticketing agency primarily in the business of selling tickets for musical concerts in the Atlanta area. TXP requested permission to sell tickets to Omni productions on a partial or entire basis on a number of occasions without success. TXP and SEATS are the only two companies which provide remote ticketing services in the Atlanta area.5 Remote ticketing services sell tickets for an event at various outlet locations throughout a metropolitan or geographical area, thereby expanding the sites where would-be spectators may buy tickets to an event beyond the box office of the facility housing the event.
Although both TXP and SEATS are engaged in the business of selling tickets to events in the Atlanta area through various outlet locations, there are some differences in how the two companies operate. TXP uses “hard tickets” which are preprinted, divided up, and distributed to various locations to be sold. SEATS, on the other hand, uses a centralized computerized system with terminals at various locations which print the ticket at the time of purchase. In addition, TXP services on a per-ticket basis are “somewhat less expensive” to promoters than the services of SEATS.6
The district court found that SEATS has sold the tickets to every musical event at the Omni since the ticketing service’s inception.7 SEATS sold more than one million tickets to Omni events between 1978 and 1982, representing a gross intake of between 9 and 13.5 million dollars in ticket sales. The court found that the major local promoters who staged concerts in the Omni during the relevant period understood from years of dealing with TOPCOL and from repeated use of the “Producer’s Agreement” that they had to use SEATS as the ticketing service for concerts at the Omni, although it also found that no promoter had actually requested approval of another ticketing agency, including TXP. In con[1413]*1413trast, the court found that some promoters used TXP a large percentage of the time for concerts performed at facilities other than the Omni.
The court did find, however, that several promoters had inquired into the possibility of “split-ticketing” — that is, where one ticketing agency (SEATS) provides only part of the ticketing services for an event, while another agency (TXP or some other hard-ticketing company) provides the balance of the ticketing.8 The court found that the defendants had a policy against split-ticketing due to the nature of their centralized computer ticketing system, but that this policy was not in any way unlawful.9
The court concluded that the lack of requests to use other ticketing agencies for entire performances was attributable to the language of the “Producer’s Agreement” and the negotiating process for use of the Omni, which “appear[ed] to indicate the necessity for using SEATS”. It described the language of the contract as falling “only slightly short of requiring promoters of concerts at the Omni to use SEATS as their ticketing service.” It also concluded that, but for the language of the contract and other incidents of negotiation between TOPCOL and promoters, at least two promoters would have used TXP on one or more occasions, although one of the two promoters would probably have been interested only in using TXP to sell a portion of the tickets in a split-ticketing arrangement with SEATS. It also concluded that there was no other credible evidence to determine what other promoters would have used TXP to sell tickets for entire performances.
Based upon these factual findings, the district court concluded that 1) the lease of the Omni facilities and the sale of tickets to Omni concerts constituted two separate products and that 2) the two products were “tied” as a matter of antitrust law “in that the lease of Omni facilities is, as a practical matter, conditioned upon use of SEATS ticket selling services”. In accordance with these findings, the court entered judgment in favor of TXP.
The district court’s order awarding relief on the basis of the defendants’ violation of Section 1 originally awarded TXP $30,624 in damages. Acting upon the defendants’ motion for additional findings of fact to clarify the basis for the damage award, the district court subsequently reduced the single damage award to $10,091.07, which was then trebled to $30,273.21. In addition, the court issued an injunction enjoining the defendants from conditioning the lease of the Omni upon the use of SEATS as a ticketing service. The terms of the injunction permitted TOPCOL to require ticketing services to post a large guarantee bond for each concert as a precondition to selling tickets for an Omni event. Finally, the district court awarded TXP $59,272.50 in attorney’s fees.
Final judgment was entered on February 4, 1986. This appeal followed.10
III. DISCUSSION
A. Antitrust Liability Under Section 1 of the Sherman Act
Section 1 of the Sherman Act prohibits “[ejvery contract, combination ... or con[1414]*1414spiracy in restraint of trade or commerce among the several States.” 15 U.S.C. § 1. The Act unequivocally endorses the economic policy of free and unfettered competition in the open market. See Northern Pacific Railway Co. v. United States, 356 U.S. 1, 4, 78 S.Ct. 514, 517, 2 L.Ed.2d 545 (1958). In carrying out the letter and spirit of the Act, the courts have consistently struck down as illegal per se certain types of actions and practices which by their nature unreasonably restrain competition and lack any redeeming virtue. Tying arrangements were placed into this category of per se anticompetitive practices long ago. Times-Picayune Publishing Co. v. United States, 345 U.S. 594, 608-10, 73 S.Ct. 872, 880-81, 97 L.Ed. 1277 (1953); International Salt Co. v. United States, 332 U.S. 392, 396, 68 S.Ct. 12, 15, 92 L.Ed. 20 (1947); see also Jefferson Parish Hospital District No. 2 v. Hyde, 466 U.S. 2, 9-10, 104 S.Ct. 1551, 1556-57, 80 L.Ed.2d 2 (1984).
A tying arrangement is “an agreement by a party to sell one product [the “tying” product] but only on the condition that the buyer also purchases a different (or “tied”) product.” Northern Pacific Railway Co., supra, 356 U.S. at 5-6, 78 S.Ct. at 518; see Amey, Inc. v. Gulf Abstract & Title, Inc., 758 F.2d 1486, 1502 (11th Cir.1985), cert. denied, — U.S.-, 106 S.Ct. 1513, 89 L.Ed.2d 912 (1986); Midwestern Waffles, Inc. v. Waffle House, Inc., 734 F.2d 705, 711 (11th Cir.1984). A tying arrangement is not illegal, however, simply because two products are sold together in the same package.11 The key to such an arrangement’s anticompetitiveness (and thus its illegality) is the seller’s ability to force buyers to purchase one product in the package, the tied product, by virtue of the seller’s control or dominance over the other product in the package, the tying product. See Northern Pacific Railway Co., supra, 356 U.S. at 6, 78 S.Ct. at 518; Times-Picayune Publishing Co., supra, 345 U.S. at 611, 73 S.Ct. at 881. As the Supreme Court stated in its most recent pronouncement on tying arrangements, Jefferson Parish Hospital v. Hyde, supra:
the essential characteristic of an invalid tying arrangement lies in the seller’s exploitation of its control over the tying product to force the buyer into the purchase of a tied product that the buyer either did not want at all, or might have preferred to purchase elsewhere on different terms.
466 U.S. at 12, 104 S.Ct. at 1558. Such an arrangement defeats free competition because it forces buyers to purchase the tied product solely because it is associated with the tying product, not because of its intrinsic superiority over competing products. See Construction Aggregate Transport, Inc. v. Florida Rock Industries, Inc., 710 F.2d 752, 780-81 (11th Cir.1983) (primary concern in tying arrangement is restriction of competition on the merits in market for tied product).
With these principles in mind, the courts have held that a plaintiff must establish the following four elements to prove that a tying arrangement is illegal per se: 1) that there are two separate products, a “tying” product and a “tied” product; 2) that those products are in fact “tied” together — that is, the buyer was forced to buy the tied product to get the tying product; 3) that the seller possesses sufficient economic power in the tying product market to coerce buyer acceptance of the tied product; and 4) involvement of a “not insubstantial” amount of interstate commerce in the market of the tied product. See Amey, Inc., supra, 758 F.2d at 1502-03; Midwestern Waffles, supra, 734 F.2d at 711-12; Kentucky Fried Chicken Corp. v. Diversified Packaging Corp., 549 F.2d 368, 375 (5th Cir.1977). Appellants challenge the district court’s conclusion that the relationship between the lease of the Omni and the use of SEATS constitutes an invalid tying arrangement on the [1415]*1415grounds that the proof at trial failed to establish three of the four requisite elements.12 We will discuss the arguments pertaining to each of the three contested elements in turn.13
1. Whether the Lease of the Omni and Use of SEATS Were “Tied”
The first and perhaps most significant issue in this appeal is the question of whether the district court correctly concluded that the lease of the Omni and the use of SEATS were “tied” as a matter of antitrust law.14 To establish that two products are in fact “tied”, a plaintiff must show something more than just that two products were sold together in the same package. Jefferson Parish, supra, 466 U.S. at 11, 104 S.Ct. at 1558; SmithKline Corp. v. Eli Lilly & Co., 575 F.2d 1056, 1061 n. 3 (3rd Cir.), cert. denied, 439 U.S. 838, 99 S.Ct. 123, 58 L.Ed.2d 134 (1978); Response of Carolina, Inc. v. Leasco Response, Inc., 537 F.2d 1307, 1327 (5th Cir. 1976). Rather, the plaintiff must establish that the seller forced or coerced the buyer into purchasing the tied product.15 See Jefferson Parish Hospital, supra, 466 U.S. at 12, 13-15, 26, 104 S.Ct. at 1558-60, 1565; Midwestern Waffles, supra, 734 F.2d at 712; Tire Sales Corp. v. Cities Service Oil Co., 637 F.2d 467, 472-74 (7th Cir.1980), cert. denied, 451 U.S. 920, 101 S.Ct. 1999, 68 L.Ed.2d 312 (1981); Response of Carolina, Inc., supra, 537 F.2d at 1327; American Manufacturers Mutual Insurance Co. v. American Broadcasting-Paramount Theatres, Inc., 446 F.2d 1131, 1137 (2d Cir.1971), cert. denied, 404 U.S. 1063, 92 S.Ct. 737, 30 L.Ed.2d 752 (1972). A showing of coercion requires evidence of actual exertion of economic muscle against the buyer which actually influences his choice of products in the tied market. See American Manufacturers Mutual Insur-[1416]*1416anec Co., supra, 446 F.2d at 1137. Part and parcel of the concept of coercion is the premise that the buyer was forced to buy a product that he did not want or would have preferred to buy elsewhere on other terms. Jefferson Parish, supra, 466 U.S. at 12, 104 S.Ct. at 1558; Will v. Comprehensive Accounting Corp., 776 F.2d 665, 669 (7th Cir.1985), cert. denied, — U.S.-, 106 S.Ct. 1659, 90 L.Ed.2d 201 (1986); Response of Carolina, Inc., supra, 537 F.2d at 1327; cf. Sports Form, Inc. v. United Press International, Inc., 686 F.2d 750, 754 (9th Cir.1982) (no tying problem where buyer asks for package of items and is sold what it wishes to buy).
Appellants argue that the district court’s conclusion that an illegal tie existed here is fatally flawed because the district court’s findings do not establish that the lease of the Omni and the use of SEATS were in fact “tied” as a matter of antitrust law. They contend that the district court’s findings of fact fall short of establishing that the appellants coerced promoters to use SEATS and that the lease of the Omni was actually conditioned on the use of SEATS. We disagree.
The district court concluded that the two “products” at issue here were “ ‘tied’ in an anti-trust sense in that the lease of Omni facilities is, as a practical matter, conditioned upon use of SEATS ticket selling services.” The district court based its ruling principally on two factors: 1) the Producer’s Agreement, which the court described as falling only “slightly” short of expressly requiring promoters to use the Omni, and 2) the negotiating process between TOPCOL and prospective promoters for use of the Omni. The court found that the combination of these two factors “appear[ed] to indicate the necessity of using SEATS”. The court also found that promoters understood through years of dealing with TOPCOL that they had to use SEATS for Omni events and that, in fact, no agency besides SEATS had ever been used to provide ticketing services for a musical event as long as SEATS had been in existence. Finally, the court found that, but for the tying arrangement, at least one promoter, Jim Veal, would have used TXP to provide ticketing services at the Omni. We hold that these findings adequately support the conclusion that the lease of the Omni and the use of SEATS were “tied” as a matter of antitrust law.
Appellants argue that these findings do not establish a “tie” because various other findings by the court undercut the conclusion that promoters were compelled to use SEATS in order to lease the Omni. Specifically, they point to findings that 1) the Producer’s Agreement did not actually require promoters to use SEATS, together with findings that none of the promoters ever asked to use another ticketing agency and none of the promoters were ever told by the appellants that they had to use SEATS, and 2) several promoters testified that they would have used SEATS regardless of the Producer’s Agreement because of the intrinsic superiority of computerized ticketing.
As to the first set of findings, we note that the fact that the Producer’s Agreement contains a clause for approval of other ticketing agencies does not necessarily dispose of the question of whether promoters were forced to use SEATS. See Northern Pacific Railway, supra, 356 U.S. at 11-12, 78 S.Ct. at 521; Midwestern Waffles, supra, 734 F.2d at 712. Where a contract or franchising agreement provides that buyers shall use only the seller or a source “approved” by the seller to purchase the tied product, the courts have looked to see if the approval clause was reasonable and permitted the buyer meaningful freedom of choice, or whether it is manipulated by the seller to force the buyer to purchase the tied product from the seller. See Midwestern Waffles, supra, 734 F.2d at 712-13; Kentucky Fried Chicken, supra, 549 F.2d at 377-79; Advance Business Systems & Supply Co. v. SCM Corp., 415 F.2d 55, 66 (4th Cir.1969), cert. denied, 397 U.S. 920, 90 S.Ct. 928, 25 L.Ed.2d 101 (1970).
Although the district court determined that the language of the approval clause in this case gave promoters the right to request approval of another ticket agency, it [1417]*1417also found that no promoter had ever requested permission to use another ticket agency, notwithstanding the approval clause, because they understood through years of dealing with TOPCOL and using the Agreement that they were required to use SEATS.16 Furthermore, it also found that the appellants had never approved another ticket agency and that they had never established written standards and procedures for approving other agencies. Cf. Kentucky Fried Chicken, supra, 549 F.2d at 378 (approval clause reasonable where seller had already approved 10 suppliers and had never refused a request for approval). Given these findings, it is reasonable to conclude that the approval clause was somewhat bogus under the circumstances present in this case and that promoters did not have meaningful freedom of choice in the tied market.
We also reject the contention that there is no “tie” here because the court found that several of the promoters would have used SEATS regardless of the tying arrangement due to their view that a computerized ticketing service is better to use for large-scale reserved seating events staged at the Omni. While it is true that two products are not tied as a matter of antitrust law if the buyer voluntarily purchases the tied product, see Will v. Comprehensive Accounting Corp., supra, 776 F.2d at 669; Response of Carolina, Inc., supra, 537 F.2d at 1327-28, the court’s findings of fact establish that at least one promoter, Jim Veal, did not use SEATS voluntarily.17 The court expressly found that, but for the tying arrangement, Veal would have used TXP for several events in the Omni. Furthermore, even if some of the promoters would have selected SEATS regardless of the tying arrangement, the arrangement prevented them from making that choice freely. We reiterate that the principal evil of tie-ins is that they foreclose competition on the merits in the tied market. See Kentucky Fried Chicken, supra, 549 F.2d at 375 (tying arrangements anticompetitive because “they may deprive the tie’s victims of the advantages of shopping around.”).
In addition, we note that the characteristics of the tied market in this case make the tying arrangement challenged here particularly destructive to competition. Although the evidence at trial indicated that computerized ticketing may have certain advantages over hard-ticketing for an arena as large as the Omni, it is unlikely that any prospective competitor in the ticketing services market would be willing or able to invest the amount of money required to develop a computerized system in light of the virtual impossibility of ever getting any of the Omni business so long as there is a tying arrangement. Cf. Northern Pacific Railway, supra, 356 U.S. at 12, 78 S.Ct. at 521 (even with approval clause, competitor in tied market at an unfair competitive disadvantage because it does not have access to tied market on same terms as seller). This disincentive is particularly real when one considers that the evidence at trial indicated that computerized ticketing appears to have no special advantage over hard-ticketing in smaller arenas, and is in many cases more expensive to use. Given the fact that the Omni is the only arena in Atlanta of a size and configuration to warrant a computerized ticketing system, a prospective competitor has no incentive to develop a computerized system at all unless he knows that he will provide at least some ticketing services for events at the [1418]*1418Omni. Cf. Jefferson Parish Hospital, supra, 466 U.S. at 13 n. 19, 104 S.Ct. at 1558 n. 19 (tying increases difficulty of entering tied market because new firms must not only match seller’s price and quality, but also offset attraction of tying product itself).
Appellants also argue that the court’s findings do not establish a “tie” because they fail in various ways to establish the element of coercion.18 First, we reject the appellants’ contention that the district court’s finding of coercion is deficient because the court did not cite a single incident of coercive or forceful “salesmanship” on their part. While it is true that the district court did not find any direct evidence attesting to the fact that the appellants put a gun to the head of promoters, the courts have never required direct evidence of coercive behavior to prove a tying violation. It is well established that coercion may be established by showing that the facts and circumstances surrounding the transaction as a practical matter forced the buyer into purchasing the tied product. Kentucky Fried Chicken, supra, 549 F.2d at 377; see Tire Sales Corp., supra, 637 F.2d at 474; Photovest Corp. v. Fotomat Corp., 606 F.2d 704, 722 (7th Cir. 1979), cert. denied, 445 U.S. 917, 100 S.Ct. 1278, 63 L.Ed.2d 601 (1980); Heatransfer Corp. v. Volkswagenwerk, A.G., 553 F.2d 964, 977 (5th Cir.1977), cert. denied, 434 U.S. 1087, 98 S.Ct. 1282, 55 L.Ed.2d 792 (1978). The district court correctly found that the facts and circumstances surrounding the negotiations for lease of the Omni, including the Producer’s Agreement, established that the “lease of Omni facilities is, as a practical matter, conditioned upon use of SEATS ticket selling services.”
We also reject the appellants’ contention that the district court improperly based its finding of coercion solely on the subjective perception of the promoters. While the subjective perception, of buyers standing alone would not be enough to support a finding of liability, Association for Intercollegiate Athletics for Women v. National Collegiate Athletic Association, 558 F.Supp. 487, 1983-1 Trade Cases para. 65,293, at 69,738 (D.D.C.1983), affd, 735 F.2d 577, 1984-1 Trade Cases para. 66,007 (D.C.Cir.1984), the district court also considered several other factors in reaching its decision, most notably the language of the Producer’s Agreement. Furthermore, the subjective understanding of the promoters that they were required to use SEATS is relevant to the determination of whether the circumstantial evidence indicates coercion and was properly weighed in that context.
Finally, we reject the appellants’ contention that proof of coercion in this case requires proof that at least some of the promoters requested permission to have TXP do their ticketing in the Omni. While, as noted earlier, coercion can be negated by a showing that the buyers bought the tied product from the seller of the tying product voluntarily, Will v. Comprehensive Accounting Corp., supra, 776 F.2d at 669; Response of Carolina, Inc., supra, 537 F.2d at 1327-28, it does not necessarily follow that a buyer has purchased the tied product voluntarily simply because he did not attempt to buy the tied product elsewhere. See Photovest Corp., supra, 606 F.2d at 725. In this case, the court found other facts tending to show that the use of SEATS was not voluntary, at least as to Jim Veal. More specifically, it found that promoters did not attempt to use other ticketing agencies because they understood from years of dealing with the [1419]*1419appellants and using the Producer’s Agreement that they were required to use SEATS and, further, that Jim Veal would have used TXP but for the tying arrangement.
2. Impact on Competition in the Tied Market
Appellants also argue that the district court’s conclusion that the practice at issue here constituted an illegal tying arrangement is erroneous because the allegedly improper practice did not have a sufficient impact on competition in the tied market to violate the antitrust laws. The parties agree that a tying arrangement will only be illegal if it affects a “not insubstantial” volume of interstate commerce in the tied market, see Jefferson Parish, supra, 466 U.S. at 16, 104 S.Ct. at 1560; Fortner Enterprises, Inc. v. United States Steel Corp. (Fortner I), 394 U.S. 495, 501, 89 S.Ct. 1252, 1257, 22 L.Ed.2d 495 (1969); Northern Pacific Railway, supra, 356 U.S. at 6, 78 S.Ct. at 518; Amey, Inc., supra, 758 F.2d at 1503, but disagree on how that volume of commerce should be measured in this case and whether that volume is sufficient to bring the conduct challenged here within the scope of the Sherman Act.
The Supreme Court has held that for purposes of determining whether the amount of commerce foreclosed in the tied market is “insubstantial”, the volume of commerce must be “substantial enough in terms of dollar-volume so as not to be merely de minimis.” Fortner I, 394 U.S. at 501, 89 S.Ct. at 1257. The relevant figure is the total volume of sales tied by the sales policy under challenge, not merely the portion of this total accounted for by the particular plaintiff who brings suit. Id. at 502. As the Supreme Court explained in Fortner I:
The requirement that a “not insubstantial” amount of commerce be involved makes no reference to the scope of any particular market or to the share of that market foreclosed by the tie ... normally the controlling consideration is simply whether a total amount of business, substantial enough in terms of dollar-volume of business so as not to be merely de minimis, is foreclosed to competitors by the tie ...
394 U.S. at 501, 89 S.Ct. at 1257. The Court further explained this standard in Jefferson Parish, stating that “[i]f only a single purchaser were ‘forced’ with respect to the purchase of a tied item, the resultant impact on competition would not be sufficient to warrant the concern of antitrust law.” 466 U.S. at 16, 104 S.Ct. at 1560.
Appellants argue that the district court found that only one promoter would have chosen TXP in the absence of the “tying arrangement” and that the loss of that promoter cost TXP only $10,091.07 in single damages. They argue that the foreclosure of a single competitor to the tune of $10,091.07 is not a substantial enough impact on commerce to implicate the antitrust laws. Appellee, on the other hand, argues that the relevant figure is the total volume of sales in the tied product market —here, the total sales of tickets to musical concerts for the relevant period. Those figures, the appellee argues, which range between 9 and 13.5 million dollars for a four-year period, do have a substantial impact on commerce.
It is clear that the relevant figure is the “total volume of sales in the tied market”, but not so clear is whether the “sales in the tied market” in this case would be the amount of ticket sales actually proven to be tied, which would be the ticket agency’s profit from Jim Veal’s ticket sales, or the amount representing all ticket sales resulting from the challenged practice, which would be the ticket agency’s profits from all ticketing services rendered for events at the Omni during the relevant period of the lawsuit. We need not resolve this question, however, because we conclude that the “not insubstantial amount of interstate commerce” test is met even by the smallest figure proffered, the $10,091.07 in actual damages to TXP flowing from Jim Veal’s promotions. Compare Microbyte Corp. v. New Jersey State Golf Association, 51 Antitrust & Trade Reg. Rep. (CCH) at 8 (D.N.J.1986) ($27,264 in [1420]*1420one year not de minimis); AAMCO Automatic Transmissions, Inc. v. Tayloe, 407 F.Supp. 430, 436 (E.D.Pa.1976) ($50,000 over 4 years not de minimis) with Amey, Inc., supra, 758 F.2d at 1503 ($325 fee “insubstantial” amount of commerce). The $10,091.07 figure represents an estimate of TXP’s profits from providing ticket-selling services for seven different events promoted by Jim Yeal — tickets sold by SEATS that would have been sold by TXP but for the tying arrangement. Although an actual tying violation was proved as to only one promoter, it involved seven different events and therefore seven different tying violations. While $10,091.07 is not an overwhelmingly large amount, particularly compared with the 9-13.5 million in total ticket sales over the relevant period, it is certainly more than de minimis.
3. Sufficient Market Power
Finally, appellants argue that TOPCOL does not have sufficient economic power to force acceptance of the tie. Sellers in an illegal tying arrangement must possess some special ability to force a purchaser to do something that he would not do in a competitive market, which is usually called “market power”. Jefferson Parish, supra, 466 U.S. at 13-14, 104 S.Ct. at 1558-59. Economic or market power over the tying product can be sufficient even though the seller does not dominate the market or the seller only exercises the power with respect to some of the buyers in the market. Fortner I, supra, 394 U.S. at 503, 89 S.Ct. at 1258. Economic power may be inferred from the tying product’s desirability to consumers or from uniqueness in its attributes. Id. at 505 & n. 2, 89 S.Ct. at 1259 & n. 2; United States v. Loew’s, Inc., 371 U.S. 38, 45, 83 S.Ct. 97, 102, 9 L.Ed.2d 11 (1962); see also Jefferson Parish, supra, 466 U.S. at 17, 104 S.Ct. at 1560 (market power can exist where seller offers unique product competitors are unable to offer). In addition, market power requires a showing that would-be competitors in the tied market cannot themselves offer the tying product on competitive terms: that is, that the seller has some cost advantage over rivals in producing the tying product or that there are substantial entry barriers into the tying product market. Fortner I, supra, 394 U.S. at 505 n. 2, 89 S.Ct. at 1259 n. 2; Spartan Grain & Mill Co. v. Ayers, 735 F.2d 1284, 1288 (11th Cir.1984), cert. denied, 469 U.S. 1109, 105 S.Ct. 785, 83 L.Ed.2d 779 (1985); see also United States Steel Corp. v. Fortner Enterprises (Fortner II), 429 U.S. 610, 617, 97 S.Ct. 861, 866, 51 L.Ed.2d 80 (1977).
Appellants argue that there are many facilities in the Atlanta area which compete with the Omni, giving any unsatisfied promoter several alternative locations to stage a production and thereby limiting the Omni’s ability to behave anti-competitively in the market. They support their argument by pointing to evidence showing that the Omni made some adjustments in its leasing arrangements to accommodate half-houses and lowered its rents in order to compete with another enclosed facility in the Atlanta area.
We reject this argument. The appellants ignore the district court’s findings that the Omni is the only enclosed facility in Atlanta capable of seating more than 4,000 and that its size and configuration make it a unique facility with substantial economic advantages for the presentation of musical concerts where the attendance is expected to be between 4,000-16,000. The clear implication from these findings is that a promoter seeking to stage a popular music concert (the kind of event TXP sells tickets for) in the Atlanta area has no other real alternative to the Omni without sacrificing the type and size of performance he or she can stage. Furthermore, TXP and other would-be competitors cannot reasonably be expected to offer the tying product themselves: ACI and TOPCOL have the exclusive right to lease the Omni, and the costs of building an arena to compete with the Omni would be more than any single competitor could bear. There is no question that the appellants have the requisite market power.
B. District Court’s Method of Calculating Actual Damages
TXP cross-appeals the district court’s award of damages. The court awarded [1421]*1421TXP approximately $10,000, an amount based upon the lost revenue from the concerts promoted by the one promoter the court found definitely would have chosen TXP over SEATS to provide ticketing services for events staged at the Omni. TXP argues that the court’s methodology in calculating the damages was flawed in two respects: 1) the court erred by refusing to calculate damages by looking at TXP’s percentage of the ticketing business at the other facilities in the Atlanta area, and 2) the court erred in refusing to calculate into the award damages derived from the promoters who the court found would have used TXP for split-ticketing.
The first argument clearly has no merit. TXP insists that the court should have used a “comparative percentage theory” to calculate its losses; that is, it should have looked to see what percentage of the ticketing business TXP held for shows staged at other facilities — facilities that were unaffected by the tying arrangement. While the courts have awarded damages in tying cases by comparing sales in the restrained market to sales in an unrestrained market, see, e.g., Zenith Radio Corp. v. Hazeltine Research, Inc., 395 U.S. 100, 123-25, 89 S.Ct. 1562, 1576-77, 23 L.Ed.2d 129 (1969), there are sound reasons why such a comparison between Omni ticketing and non-Omni-ticketing would be inappropriate in this case. The court found that the Omni was a unique facility due to its size and configuration: while it can seat up to 16,000, the next largest enclosed facility in the City can seat only 4,000. As the testimony at trial indicated, the ticketing needs for an event for 3,000 or 4,000 people are quite different from the ticketing needs for an event for 15,000 people.
This potential difference is important when one considers the qualitative difference between the hard-ticket services provided by TXP and the computerized ticketing services provided by SEATS. Many of the promoters indicated that they would not consider using a hard-ticketing service for a reserved seating show at a facility as large as the Omni, although they would consider using split-ticketing and would not hesitate to use hard-ticketing for a smaller arena.
TXP’s second argument is also meritless. In considering the damages award, the court only considered events staged by the single promoter, Jim Veal, who testified that he would have used TXP for full ticketing, and disregarded events staged by promoters who testified that they would have only used TXP for split-ticketing. The court apparently did this on the basis of the following reasoning19: 1) SEATS had a permissible policy against split-ticketing; 2) given this policy, promoters would have been in a position of selecting either SEATS or TXP for the entire ticketing; and 3) given this choice, there was no evidence that any of the promoters with the exception of promoter Jim Veal would have chosen TXP for full ticketing; in fact, the promoters indicated that they would not choose TXP to ticket a facility as large as the Omni;20 and 4) consequently, the only actual damages TXP proved were those associated with the loss of Veal’s business.
TXP challenges this reasoning, primarily on the basis that there was no finding by the court that the other promoters would in fact have selected SEATS if forced to choose between SEATS and TXP.21 Indeed, it appears that the district [1422]*1422court did not in fact make an express finding to that effect: it found only that there was not “sufficient credible evidence to determine what other promoters would have used plaintiffs services for entire performances.”
Concededly, this finding is not an affirmative statement that every other promoter besides Jim Veal would have chosen SEATS to do full ticketing in the absence of the tying arrangement, but a statement that there is not enough evidence to determine what every promoter who has used the Omni during the relevant period would have done. Nonetheless, it does not provide a basis for awarding damages, as the plaintiff contends. Furthermore, many of the promoters testified at trial that they would not use hard-ticketing at the Omni, which means that they would have to use SEATS, although this testimony was not incorporated into the court’s findings of fact. Given the lack of conclusive proof that other promoters would have used hard-ticketing systems in the Omni, we hold that the district court reasonably awarded damages based upon what was proven regarding the single promoter who the court found would in fact have used TXP but for the antitrust violation.
C. Injunctive Relief
TXP also cross-appeals an aspect of the injunctive relief awarded by the district court. The court issued an injunction against the appellants prohibiting them from requiring promoters to use SEATS, but included a provision permitting the appellants to require all agencies providing ticketing services for Omni events to post a $150,000 bond.22 The court imposed the bonding requirement based upon findings that the Omni has a legitimate interest in the safety of ticket proceeds and in the financial integrity of the agencies handling the ticket proceeds. TXP challenges the portion of the injunction that permits the appellants to require agencies to post a bond because: 1) the bond effectively deprives TXP of a remedy for the appellants' misconduct because it and other small agencies cannot afford a bond; 2) the Omni’s concerns for security could be satisfied by requiring the promoter to post the bond rather than the ticketing agency, since the promoter is the party that actually contracts with the Omni, not the ticketing agency; and 3) no other facility (presumably in Atlanta) requires the posting of a bond.
We see nothing inappropriate or unreasonable in the district court’s order for injunctive relief. As the Supreme Court noted in United States v. Loew’s, Inc., supra, “the trial judge’s ability to formulate a decree tailored to deal with the violations existent in each case is normally superior to that of any reviewing court, due to his familiarity with testimony and exhibits.” 371 U.S. at 52, 83 S.Ct. at 105-06; see also International Salt Co., supra, 332 U.S. at 400-401, 68 S.Ct. at 17. Given the court’s recognition of TOPCOL’s legitimate interest in preserving the safety and integrity of the box office, which TXP does not challenge, the bonding requirement is an attempt to protect the legitimate interests of the appellants without giving them too much control over the actual selection of ticket agencies. In essence, the bonding requirement is a substitute for allowing TOPCOL to “approve” prospective ticket agencies, which was the procedure originally in place to protect the integrity of the box office proceeds.23
Furthermore, a bond of $150,000 does not appear as onerous as TXP makes it out to be, particularly given the millions of dollars in box office proceeds a ticket agency would process for a capacity crowd at the Omni. Finally, the fact that no other facility requires a bond is not particularly significant since no other facility in Atlanta has nearly the seating capacity of the Omni. A smaller seating capacity trans[1423]*1423lates into a reduced sum of money at risk at any given time, which correspondingly reduces the need for security measures such as bonding requirements.
D. Attorney’s Fees
Both parties appeal the district court’s award of $59,272.50 in attorney’s fees to TXP. The appellants claim that the district court clearly erred because it gave the plaintiff an amount greater than the amount TXP was contractually obligated to pay its attorneys. TXP claims that the district court clearly erred in reducing the loadstar solely on the basis of the low damage award. We reject both arguments and affirm the district court’s award.24
The fee agreement between TXP and its counsel provided that counsel would receive one third of the total judgment, with no portion of the attorney’s fees awarded by the court going to TXP. Over the objection of the appellants, the district court decided to determine a “reasonable” fee by applying the twelve factors articulated in Johnson v. Georgia Highway Express, 488 F.2d 714 (5th Cir.1974), without regard to the contingency fee agreement. Accordingly, the court analyzed TXP’s fee request in light of the Johnson guidelines and calculated the plaintiff’s loadstar at $118,545, concluding that the hours expended and rates charged were reasonable. The court then reduced the loadstar by a negative multiplier of .5 based upon the limited success of the litigation reflected in the small damage recovery, to reach the final award of $59,272.
Appellants argue that the district court could not award any more than the amount called for in the contract between the parties, citing a series of cases for the proposition that a litigant should not be awarded an amount in attorney’s fees greater than the amount he is contractually obligated to pay. See Pharr v. Housing Authority of the City of Prichard, 704 F.2d 1216, 1217-18 (11th Cir.1983); Johnson v. Georgia Highway Express, supra, 488 F.2d at 718. The rationale for such a rule is to avoid giving the plaintiff a windfall in a situation where the plaintiff keeps for himself the portion of the fee award which exceeds the amount he is contractually obligated to pay his attorneys. Computer Statistics, Inc. v. Blair, 418 F.Supp. 1339, 1351 (S.D.Tex. 1976); see also Exhibitors’ Service, Inc. v. American Multi-Cinema, Inc., 583 F.Supp. 1186, 1190-91 (C.D.Cal.1984), rev’d on other grounds, 788 F.2d 574 (9th Cir. 1986).
We reject the appellants’ argument on two grounds. First, the terms of the fee agreement in this case undercut the rationale for the rule limiting fee awards to the amount of the fee agreement. Since the plaintiff in this case has agreed that it will not keep any portion of the court’s attorney’s fee award, there is no risk of a windfall to the plaintiff.
Second, the policies behind the statutory provision for an attorney’s fee award to private litigants in Sherman and Clayton Act cases would be defeated by rigid application of the contract limitation rule articulated in Johnson and Pharr to antitrust lawsuits.25 Section 4 of the Clayton Act entitles a successful plaintiff as a matter of right to “recover threefold the damages by him sustained, and the costs of suit, including a reasonable attorney’s fee.” 15 U.S. C.A. § 15; 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); State of Illinois v. Sangamo Construction Co., 657 F.2d 855, 857-58 (7th Cir.1981); Carpa, Inc. v. Ward Foods, Inc., 536 F.2d 39, 52 (5th Cir.1976). Sections 4’s purpose is [1424]*1424three-fold: 1) to encourage private citizens to undertake enforcement of the antitrust laws; 2) to insure that the cost of doing so does not diminish the plaintiff’s treble damages award; and 3) to require a losing defendant to pay the plaintiff’s attorney’s fees as part of the penalty for violating the antitrust laws. Ohio-Sealy Mattress Manufacturing Co. v. Sealy, Inc., 776 F.2d 646, 661 (7th Cir.1985); Twin City Sportservice, Inc., supra, 676 F.2d at 1312; Farmington Dowel Products Co. v. Forster Manufacturing Co., 421 F.2d 61, 90 (1st Cir.1970). In recognition of these policies, several courts have questioned the propriety of contingency fee arrangements in Sherman Act cases or, even further, have held that the determination of what constitutes a reasonable fee should be made without reference to any prior fee agreement.26 See Sangama Construction Co., supra, 657 F.2d at 861-62; Pitchford v. Pepi, Inc., 531 F.2d 92, 110-111 (3rd Cir.1975), cert. denied, 426 U.S. 935, 96 S.Ct. 2649, 49 L.Ed.2d 387 (1976); Farmington Dowel Products Co., supra, 421 F.2d at 89 n. 61; Black Gold Ltd. v. RockWool Industries, 529 F.Supp. 272, 274 (D.Colo.1981).
We find the reasoning by these courts persuasive and agree with the results of that reasoning. While a prior fee agreement may sometimes be a useful indication of what the parties believe to be a reasonable fee, it obviously fails to do so where the fee agreement is contingent and the damage award is small. Enforcing the fee agreement in these circumstances not only would discourage competent counsel from representing private litigants in antitrust suits, but would provide a windfall to the appellants rather than penalize them. Given the terms of this particular fee agreement, the size of the damage award in this case, and the policies behind Section 4 of the Clayton Act, we hold that the district court properly calculated a reasonable attorney’s fee based upon the twelve Johnson factors without regard to the contingent fee agreement between the plaintiff and its attorney.
TXP argues that the district court erred in reducing the loadstar amount solely because of a small damage award. While the proposition that a small damage award alone does not justify reducing a fee award is correct, see Amey, Inc., supra, 758 F.2d at 1509; see also West v. Capitol Federal Savings & Loan Association, 558 F.2d 977, 981 (9th Cir.1977), the district judge did not in fact reduce the fee solely on the basis of the small damage award. Instead, he made a determination that the plaintiff had achieved only limited success in the suit, evidenced by the fact that TXP was only able to prove actual damages from seven out of ninety concerts staged at the Omni during the relevant time period. Unlike a damage award in a torts ease, the damage award here was somewhat related to the plaintiff’s degree of success in the case. It is well established that the result obtained from a lawsuit — the degree of success — is a relevant consideration in reducing or enhancing a loadstar. Hensley v. Eckerhart, 461 U.S. 424, 435-36, 103 S.Ct. 1933, 1940-41, 76 L.Ed.2d 40 (1983); Johnson v. Georgia Highway Express, supra, 488 F.2d at 718. The district court did not abuse its discretion in applying a negative multiplier in this case.
For the foregoing reasons, we affirm the district court on all the issues presented in this appeal.
AFFIRMED.