Opinion for the Court filed by Circuit Judge WALD.
WALD, Circuit Judge:
These appeals spring from a series of pre-trial rulings by the district court in' three consolidated antitrust cases involving wax museums; the effect of these rulings is to deny all relief on the claims filed. Plaintiff-appellants are commonly owned corporations which operate wax museums in Williamsburg, Virginia, Gatlinburg, Tennessee, and Gettysburg, Pennsylvania. Between 1962 and 1967, all three appellants entered into agreements to purchase or lease display figures for their museums from appellees and to become appellees’ “franchisees.” In 1977, the appellants filed antitrust claims alleging that the appellees illegally tied the franchise arrangements to the initial sale or lease of the wax figures. Appellants National Souvenir Center, Inc. and Historic Reviews, Inc., which jointly run the Gatlinburg museum, also claimed that appellees unlawfully exercised their monopoly power in the wax figure market to require leasing rather than selling the figures. Upon filing suit, all appellants stopped paying the franchise fees and rents required by the allegedly illegal agreements. Appellees then counterclaimed for recovery of overdue payments and interest.
The district court made several rulings relevant to the issues involved in this appeal. It first denied appellants’ motion that appellees’ attorneys be disqualified because they had previously represented one plaintiff in matters allegedly related to negotiation of one of the agreements at issue here. It then denied appellees’ motion for summary judgment based, on their claim that the antitrust charges were patently insubstantial, but granted them summary judgment on their contract counterclaims, awarding them the overdue franchise and lease fees, prejudgment interest on those fees, and ordering the appellants to pay all future franchise fees as they become due. Finally, the court granted summary judgment for the appellees on the ground that the antitrust claims were barred by the statute of limitations. The appellants appeal all adverse rulings including the remedial order requiring them to pay overdue franchise fees with interest and all future fees as they become due.
We affirm the dismissal of the appellants’ tying claims on statute of limitations grounds. We find, however, that the statute of limitations is not a proper ground for dismissing the Gatlinburg appellants’ monopoly leasing claim. Although we do not wholly agree with the district court’s analysis of the applicability of the appellants’ antitrust defenses to appellees’ counterclaims for overdue franchise fees and lease payments, we agree with the court that those defenses may not be raised, given the facts of these cases. Therefore, we affirm the award of past due franchise and lease payments. We do not find, however, that the district court sufficiently justified its order requiring appellants to pay future franchise fees as they become due. The result is a remand for further proceedings on the Gatlinburg monopoly leasing claim and of the order to make future payments.
I. Background
A. The Franchise Relationship
This lawsuit was spawned in January, 1957, when Frank Dennis incorporated appellee Historic Figures, Inc. (Historic) to operate a wax museum in Washington, D.C. The display figures in the museum were provided by appellee Lynch Display Corporation (Lynch), a company formed by appellee Earl Dorfman in March, 1957, to manufacture such figures. The figures were made of a vinyl plastic material rather than the traditional beeswax and, according to the appellants, “were considered a substantial improvement over the true wax figures.” Brief for Appellants at 15. Lynch agreed to provide the figures for the Washington museum and to assist in installing them in appropriate historical settings. In return, Historic agreed to purchase figures exclusively from Lynch and, for a five year [226]*226period, to act as Lynch’s sales agent to other wax museums.1
Historic soon expanded its business to “franchising” museums in different parts of the United States. The first franchise was granted by Historic’s subsidiary National Historical Museums, Inc. (NHM), in 1960, to appellant-National Civil War Wax Museum (Gettysburg), which was owned primarily by Chaim Uberman. According to Dennis’s affidavit accompanying appellees’ first motion for summary judgment, the agreement between NHM and Gettysburg obligated NHM to provide Lynch figures at cost, and to “furnish, at Gettysburg’s request, services ‘in connection with the establishment of a museum by franchisee’ including historical research for the figures and display scenes, advice on the cast of characters, and story line, assistance in planning floor layouts and advice on promotional material and operating procedures.” Brief for Appellees at 9. The appellants contend, however, that NHM also was obligated to “provide continuing franchisor services to its franchisees in the form of assistance in the efficient operations of the museum” throughout the twenty year franchise relationship. Brief for Appellant at 21. In return, Gettysburg agreed to pay NHM 5% of its annual gross receipts for twenty years, beginning in April, 1962, when the museum opened.
In May, 1962, NHM entered a similar agreement with appellant Historic Reviews, Inc. (Gatlinburg). NHM agreed to provide essentially the same service as it provided Gettysburg in return for 5% of Gatlinburg’s gross receipts for the nineteen year four month term of the agreement. Unlike Gettysburg, Gatlinburg did not purchase the display figures from Historic, but rather leased them directly from Lynch for the term of the agreement for an annual minimum rent plus 15% of gross annual receipts over $100,000. NHM also agreed not to grant another wax museum franchise within 200 miles of Gatlinburg during the term of the agreement.2
Uberman established a third franchised wax museum in Williamsburg, Virginia. NHM and appellant Williamsburg Wax Museum, Inc. (Williamsburg) entered a franchise agreement on September 22, 1967. NHM obligated itself to provide the same services as for Gettysburg and Gatlinburg, and not to franchise another wax museum within 100 miles of Williamsburg. In return, Williamsburg agreed to pay NHM 5% of its gross receipts for twenty years, and 2V2% of gross receipts thereafter.
The agreements are not typical franchises. See Brief for Appellants at 20; Brief for Appellees at 12-13. As the district court recognized:
[Tjhe characteristics that generally typify a franchise are not present here: there is no operation under a common name or designation, no cooperative advertising, no periodic inspections, and no establishment of common standards or business practice.
Williamsburg Wax Museum, Inc. v. Historic Figures, Inc., Civ. No. 77-0093, slip op. at 3 n. 5 (May 19, 1981) (Memorandum Order granting defendants’ motion for summary judgment on their counterclaims, but denying summary judgment for defendants on plaintiffs’ antitrust claims). Indeed, precisely what NHM provided in return for the “franchise fee” is a critical issue in the case. Appellees characterize the franchise agreements as
intended to get the museums off the ground by providing experienced assistance “in connection with the establishment of a wax museum” and by offering Dorfman’s consultant services to the franchisees for this purpose only for the period prior to and during the opening of each museum. ... Thereafter, NHM and Dorfman were obligated during the terms of the agreements “to stand by” to provide additional services [227]*227as requested and paid for by the franchisees (and with respect to Gatlinburg and Williamsburg, also were under a continuing obligation not to establish competing wax museums in specified geographical areas) but the franchisees were under no obligation either to request or pay for such additional services.
Brief for Appellees at 13. The appellants’ interpretation of the agreements, on the other hand, is quite different. They claim that “actual services, not merely a standby commitment, were due from the defendants for the franchise fee payments, but that the defendants generally failed to honor this obligation.” Brief for Appellants at 20. The record, however, shows no particular instance where NHM provided additional services, beyond start-up services, except for an additional charge.
B. The District Court Rulings
The district court first considered appellants’ motion to disqualify defendants’ counsel, Covington & Burling (C & B), on the ground that it had previously counselled one appellee, Gettysburg, regarding the franchise agreement involved in this suit. Williamsburg, 501 F.Supp. 326, at 328 (Nov. 26, 1980) (Memorandum). The district court’s inquiry focused on whether “there is a substantial relationship between the present litigation [involving the franchise agreements] and the matters on which C & B previously provided advice to Gettysburg.” Id. at 328. After examining the record before it, the court denied appellants’ motion to disqualify C & B on the ground that “there is not the slightest evidence or even suggestion in all these materials that C & B advised Gettysburg with respect to the franchise agreement.” Id. at 329.
The district court next turned down appellees’ motion for summary judgment on appellants’ antitrust claims. It noted that the elements of a per se tying violation under Section 1 of the Sherman Act, 15 U.S.C. § 1, are
(1) that the challenged arrangement is in fact a tying arrangement, (2) that the seller has sufficient economic power with respect to the tying product, and (3) that a “not insubstantial” amount of interstate commerce in the tied product is affected.
Williamsburg, slip op. at 5-6 (May 19, 1981) (Memorandum Order). It found there were genuine issues of material fact on all three elements. First, it rejected appellees’ “attempts to analogize these cases to traditional franchise cases” involving a single product or products that go “hand-in-hand with [each] other,” id. at 7 n. 10, observing that whether the “franchise” and figures were so related that they constituted a single product was a genuinely disputed issue of fact. Second, it was not able to find that the Lynch display figures were “not sufficiently unique” or that “satisfactory substitutes were available,” and that therefore appellees did not have a monopoly in the tying product market. Finally, it could not conclude that the franchise fees NHM collects affected only an “insubstantial” amount of interstate commerce. On the basis of such factual disputes, the district court declined to rule that appellants’ per se tying claim was invalid as a matter of law.
The district court, however, did grant summary judgment for appellees on their counterclaims. It initially interpreted Kelly v. Kosuga, 358 U.S. 516, 79 S.Ct. 429, 3 L.Ed.2d 475 (1959), and Mullins v. Kaiser Steel Corp., 642 F.2d 1302 (D.C.Cir.1980), rev’d, 455 U.S. 72, 102 S.Ct. 851, 70 L.Ed.2d 833 (1982), to preclude a defense to a contract action in a case such as this based on the illegality of the contract under the antitrust laws, because the illegality defense was limited to situations where “enforcement ... would make the court a party to the illegality.” Williamsburg, slip op. at 10 (May 19, 1981) (Memorandum Order). After the Supreme Court reversed this court’s ruling in Kaiser, 455 U.S. 72, 102 S.Ct. 851, 70 L.Ed.2d 833, it reconsidered, but concluded, once again, that as long as “the promise being sued on is not itself illegal under the antitrust laws,” Kaiser did not require recognition of the defense. Williamsburg, slip op. at 2 (Sept. 3,1982) (Memorandum). The promise to pay being sued on in this case [228]*228was not itself illegal, the district court said, since any antitrust damages in this case “would not necessarily include a recovery of the fees paid by plaintiff under the contract.” Id. at 3. It thus refused to vacate the grant of summary judgment for appellees. Subsequently, the district court ordered that appellants pay all overdue charges due under the agreement, plus prejudgment interest on them, Williamsburg (Nov. 4, 1982) (Order adopting plans for stay of final judgment entered September 3, 1982), as well as all future charges as they become due.
The district court finally dismissed appellants’ antitrust claims-in-chief as barred by the Clayton Act’s four year statute of limitation, 15 U.S.C. § 15b. See Williamsburg, 554 F.Supp. 182 (D.D.C.1982) (dismissing tying claims); National Souvenir Center, Inc. v. Historic Figures, Inc., Civ. No. 77-1243 (Jan. 31, 1983) (Memorandum dismissing suit based on unlawful use of monopoly power). It reasoned that since the agreements were executed well over four years before appellants filed suit, they were barred unless appellees committed new “overt acts” within the limitations period which caused antitrust injury. Finding none, the court dismissed the suits.
Appellants appeal from all the adverse rulings of the district court. In addition, they also ask us, in remanding, to reverse the district court’s consolidation of these three cases, claiming that such consolidation may create confusion for a jury. We turn now to consider the merits of these appeals.
II. The Statute of Limitations
Appellants brought their antitrust claims under the treble damage provision of the Clayton Act, 15 U.S.C. § 15. Section 4B of that Act provides:
Any action to enforce any cause of action under sections 15 or 15a of this title shall be forever barred unless commenced within four years after the cause of action accrued.
15 U.S.C. § 15b. The primary question in this appeal is when the appellants’ cause of action “accrued.”
We assume for purposes of this issue, as the district court did, that appellants’ complaints state a valid cause of action. It follows, then, that appellants could have raised their antitrust claim as soon as the allegedly unlawful agreements were executed and they suffered harm therefrom. But this does not mean their cause of action necessarily “accrued” only at that time. In Hanover Shoe, Inc. v. United Shoe Machinery Corp., 392 U.S. 481, 502 n. 15, 88 S.Ct. 2224, 2236 n. 15, 20 L.Ed.2d 1231 (1968), the Supreme Court held that although an unlawful lease-only policy first affected the plaintiff in 1912, a suit instituted in 1955 was not barred by Pennsylvania’s six year statute of limitations, since the lease-only policy was “conduct which constituted a continuing violation of the Sherman Act .. . [and] inflicted continuing and accumulating harm on Hanover.” Id. The “continuing violation” exception to the rule that the action accrues at the time the initial violation first injures the plaintiff was further delineated by the Court in Zenith Radio Corp. v. Hazeltine, Inc., 401 U.S. 321, 91 S.Ct. 795, 28 L.Ed.2d 77, which stated:
[i]n the context of a conspiracy to violate the anti-trust laws, ... each time a plaintiff is injured by an act of the defendants a cause of action accrues to him to recover the damages caused by that act and that, as to those damages, the statute of limitations runs from the commission of the act.
Id. at 338, 91 S.Ct. at 806. Under Zenith and Hanover Shoe, then, any act within the limitation period that effectuates an antitrust injury pursuant to the conspiracy [or in this case the agreement] gives rise to an action for damages. For their action to survive, plaintiff-appellants had to show an “overt act” pursuant to the original tying arrangement by the appellees within the limitation period which caused them an antitrust injury. See Kaiser Aluminum & Chemical Sales, Inc. v. Avondale Shipyards, Inc., 677 F.2d 1045, 1055-56 (5th Cir.1982), cert. denied, 459 U.S. 1105, 103 S.Ct. 729, 74 L.Ed.2d 953 (1983); Electroglas, Inc. v. [229]*229Dynatex Corp., 497 F.Supp. 97, 105 (N.D.Cal.1980).
In the case of a genuine tying arrangement, the “overt act” requirement may be satisfied merely by the parties continuing to maintain contractual relationships that directly affect competition in the tied product market. See, e.g., Twin City Sportservice, Inc. v. Charles O. Finley & Co., 512 F.2d 1264, 1270 (9th Cir.1975); Electroglas, 497 F.Supp. at 105; Aamco Automatic Transmissions, Inc. v. Tayloe, 407 F.Supp. 430 (E.D.Pa.1976); Material Handling Industries, Inc. v. Eaton Corp., 391 F.Supp. 977, 980 (E.D.Va.1975). This is because the evil of a tying arrangement is that it allows a seller who has monopoly power in the tying product market to use it as leverage to gain a share of the tied product market. See Fortner Enterprises, Inc. v. United States Steel Corp., 394 U.S. 495, 498, 89 S.Ct. 1252, 1256, 22 L.Ed.2d 495 (1969); Northern Pacific Rail Co. v. United States, 356 U.S. 1, 5-6, 78 S.Ct. 514, 518-19, 2 L.Ed.2d 545 (1958). In so doing, the monopolist forecloses the share of the secondary market involved in the tying arrangement from competitors, and in addition is able to charge more for the tied product than the purchaser would have paid absent this leverage. Tying arrangements, even if not strictly enforced, “are binding obligations held over the heads of vendees which deny defendants’ competitors access to the fenced-off market on the same terms as the defendant.” Northern Pacific, 356 U.S. at 12, 78 S.Ct. at 521. They effectively transfer the seller’s monopoly leverage in the tying market to contractual obligations in the tied market. The critical issue thus becomes whether the agreements, or appellees’ actions pursuant thereto, obligated appellants to deal only with appellees or otherwise discouraged appellants from turning to other suppliers in the tied product market within the statute of limitations period.
To make this determination, we have first to identify the “tied product.” At oral argument appellees’ counsel characterized it as “the franchise.” As best we can fathom, he meant the long-term association with NHM along with the start-up advice and stand-by availability that was sold to appellants at the time the agreements were executed. The appellants, on the other hand, specifically alleged that the tie-in was of promotion, advertising and other services related to museum operations which appellees were obligated to provide appellants in payment for their franchise fees. If the appellees are correct, then performance of the agreement, even if it involved an initial tie-in, would have no anticompetitive effect on the market thereafter and so would not survive the statute of limitations bar.
The district court, in granting summary judgment for appellees, found in favor of their contention that the agreements did not call for the appellees to provide promotional, advertising or other operation-related services during the limitation period in return for the franchise fees. The district court, however, apparently did not review the record to ensure that this was not a disputed issue. Instead it asserted that, “[i]t is the law of these cases that the parties intended any post start-up services to be paid for separately, over and above the ongoing franchise fees,” relying on its statement in an earlier Memorandum Order of May 19, 1981, that
[u]nder the “franchise” agreements, defendants were obligated to provide various start-up services or products, and they agreed to “make themselves available” to provide further services at additional cost, in exchange for a fee of five percent of the franchisee’s annual gross receipts.
Williamsburg (Memorandum Order granting summary judgment in part and denying it in part).3
[230]*230In the proceedings leading to the order of May 19, 1981, however, the parties did not litigate whether the tied product was start-up services and a standby commitment, or provision of promotions and advertising without further costs throughout the term of the agreement. For the appellants to survive summary judgment on the viability of their antitrust claims, they had to show only that there were factual issues about whether there was a separate product that was tied to the purchase of the museum figures, and whether appellees had a monopoly on those figures. Because the factual issue of whether the tied product was to be provided throughout the term of the agreement, as opposed to at the beginning only, was immaterial to the court’s disposition in its May 19th order, the law of the case doctrine does not apply. See Russell v. Commissioner of Internal Revenue, 678 F.2d 782, 784-85 (9th Cir.1982) (dictum in prior decision “is not part of the law of the case”). However, we affirm the district court on a different basis. We conclude that the record before the court on the summary judgment motion does not support the appellants’ contention that there is a genuine issue of fact regarding the appellees’ obligations to provide continuing services for the basic franchise fee throughout the term of the agreements.4 Hence, the district court’s critical assumption that the agreements did not so provide was valid.
Turning to the record on the scope of the agreements, we look first and foremost at the terms of the franchise agreements themselves. Appellants contend that each agreement “on its face” obligates the appellees to provide continuing services for the basic franchise fee. See Reply Brief for Appellants at 8. We do not agree. The Gettysburg agreement, which is typical of all three agreements, provides:
[NHM] will advise FRANCHISEE regarding the scenes and figures to be displayed in FRANCHISEE’S museum, the selection of a museum site, the layout designs, and other similar problems which may arise in connection with the establishment of a museum by FRANCHISEE. [NHM] will also advise FRANCHISEE regarding administrative procedures for the efficient operation of FRANCHISEE’S museum, including accounting procedures, turnstile and ticket operations, building maintenance, and promotion and advertising techniques. In connection with such advice, [NHM] will make available to FRANCHISEE the services of a qualified individual for two consultation periods, not to exceed one week each in duration at FRANCHISEE’S request during the period ending 30th day of SEPTEMBER, 1962. . ..
In consideration of the unique figures and the services to be furnished by [NHM], FRANCHISEE agrees to pay to [NHM] for a period of Twenty (20) years following the date of the opening to the public of FRANCHISEE’S museum an amount equal to Five per cent (5%) of the gross admission income received by FRANCHISEE from the operation of its museum.
This key passage from the agreement indicates to us that NHM did not obligate itself to provide continuing services over the years as the franchise agent. It provides for advice relating to the “establishment of a museum" and “administrative procedures for the efficient operation” including advice on “promotion and advertising techniques.” (Emphasis supplied). It also sets out the extent of the services to be rendered “in [231]*231connection with such advice,” i.e., it was not to exceed two weeks of consultation during the period ending September 30, 1962. Although there is no set term for the franchise itself, the agreement requires Gettysburg to pay a fee for twenty years. It seems clear that most of this fee is an extended payment for the Lynch figures. Only a tortuously strained interpretation of this language supports appellants’ contentions that NHM was obligated to provide, as well, an undefined and open-ended amount of promotion, advertising and other museum services throughout the twenty year period without further pay.
Appellants point, additionally, to the affidavit of Saul Eric Uberman, to demonstrate appellees’ continuing obligation to provide services. But Saul Uberman, the son of Chaim Uberman and vice president of C.M. Elberman Enterprises, Inc., the corporate successor of the appellants, was not involved in negotiating any of these agreements. Beyond the assertion that “it was never the understanding of either Frank Dennis nor of Earl Dorfman that the franchisor’s obligations under the three franchise agreements were limited to merely a stand-by commitment,”5 3 SRE at 690, his affidavit suggests that certain meetings and telephone contacts between appellants and appellees that cannot be tied to additional fee payments might be evidence of provision of additional services under the agreements.6 Id. at 610. This obviously is pure speculation. The affidavit concludes by noting that Saul Uberman had requested services from Frank Dennis and Earl Dorfman on several occasions, but that they did not comply with these requests. Appellants place great significance on the fact that neither Dennis nor Dorfman ever stated in reply to these requests that the services would not be provided because they had to be paid for separately. See id. at 611. This second negative inference, however, is as speculative as the first.
Reviewing the record as a whole, we find most striking the appellants’ inability to point to a single concrete instance before suit was filed when appellees either provided services within the limitations period for no additional fee, or appellants complained that the lack of such free services breached the agreements. In the end, we simply find these bits and pieces and the reasonable inferences drawn from them, even when viewed in the light most favorable to appellants, insufficient to raise a genuine issue of material fact as to whether the agreements obligated the appellees to provide advertising and promotional services on a continual basis over the life of the franchise without additional compensation.
After concluding that the tied product was only initial start-up services, the district court inquired into the agreement’s ongoing anticompetitive effects and determined that the appellants suffered “only pecuniary and not antitrust harm within the limitations period.” Williamsburg, 554 F.Supp. at 184. We agree with the district court that mere receipt of payments under an agreement that at some time had anticompetitive effects on the tied product market but no longer has such effects, does not cause “antitrust harm,” and does not constitute a continuing antitrust violation. As the district court pointed out,
[i]f the law were otherwise, the statute of limitations would have little force whenever a contract allegedly executed in violation of the antitrust laws provided for long term payments: there would be no repose until four years after the last installment payment.
[232]*232Williamsburg, 554 F.Supp. at 184. We also agree with the district court that appellees’ commitment to stand by and provide services at fair market value would not seem in any way to discourage the appellants from purchasing the allegedly tied services from other sellers of comparable services, and so would not inhibit competition in the tied market. Because no “overt act” in the four years preceding appellants’ suit had any effect on the market, we affirm the district court’s grant of summary judgment as to the tying claims on statute of limitation grounds.
We do not agree, however, with the district court’s subsequent dismissal on statute of limitations grounds of Gatlinburg’s claim that it was forced to lease the Lynch figures as part of appellees’ conspiracy to monopolize the wax museum display figure market. See National Souvenir Center, Inc. (Jan. 31, 1983) (Memorandum granting appellees summary judgment on monopolization claims based on Gatlinburg lease on statute of limitations grounds). Appellants alleged that the Gatlinburg lease, like the leases found illegal in Hanover Shoe, 392 U.S. at 486 n. 3, 88 S.Ct. at 2227 n. 3, perpetuated appellees’ monopoly power in the wax figure market. See Brief for Appellants at 54. They say that the required lease discouraged them from exercising “independent judgment” about whether to dispose of the Lynch figures and replace them with competitors’ products at any time in the future and so reinforced appellants long-term monopoly position. See Brief for Appellants at 53-54; cf. Hanover Shoe, 392 U.S. at 507, 88 S.Ct. at 2238-2239 (appendix to opinion of the court). We admit to extreme skepticism about the substantive validity of this monopoly lease claim based on maintenance of a single lease by an alleged monopolist.7 We are aware of no case recognizing such a claim. Appellees’ sale of the Lynch figures to other wax museum franchisees seriously undercuts appellants’ arguments that appellees relied on the lease as a mechanism to discourage replacement of the figures with those of competitors during the lease term, or that leasing rather than selling significantly affected the market for figures.8 Nonetheless, we are not asked here to review the substantive validity of Gatlinburg’s claim, only the propriety of its dismissal on statute of limitations grounds.
Our test for determining tvhen an antitrust cause of action stops “accruing” requires us to look at when the challenged contract—in this case the lease—ceases to obligate conduct that has anticompetitive [233]*233effects. Requiring appellants to continue paying rent for the Lynch figures meant they could not resell the figures or replace them throughout the duration of the lease without severe economic losses; it had as much effect in the market for the figures in 1977, as it did in 1962. Because of this continuing allegedly “anticompetitive” effect of the lease, the statute of limitations is not a proper ground for dismissing the monopolization claims stemming therefrom. See Hanover Shoe, Inc. v. United Shoe Machinery Corp., 245 F.Supp. 258, 296 (M.D.Pa.1965) (“recovery for payments made [within the limitations period] pursuant to leases executed prior to that [period] is not barred by the .. . statute of limitations”), vacated and remanded on other grounds, 377 F.2d 776 (3d Cir.1967), aff’d in relevant part, rev’d in part and remanded, 392 U.S. 481, 88 S.Ct. 2224, 20 L.Ed.2d 1231 (1968).
III. Antitrust Defenses to Contract Counterclaims
Appellants also assail the district court’s grant of summary judgment on the appellees’ claims for overdue franchise and lease payments. They claim that the judgment requires a federal court to enforce an illegal contract and that result is contrary to the rule governing antitrust defenses recently laid down in Kaiser Steel Corp. v. Mullins, 455 U.S. 72, 102 S.Ct. 851, 70 L.Ed.2d 833 (1982). The district court read Mullins as allowing antitrust defenses to contract suits only where “the promise being sued on is itself illegal” under the antitrust laws. It characterized the promise appellees sued on as one “for monies for goods or services furnished to the plaintiff over a period of years.” Williamsburg, slip op. at 2 (Sept. 3, 1982) (Memorandum). It apparently concluded that this promise was legal because the “damages [Gatlinburg asked for in its antitrust claim] would not necessarily include a recovery of the fees paid and to be paid by [Gatlinburg] under the contract.” Id. Although our reasoning differs from that of the district court, we agree that under Mullins appellants cannot raise their antitrust defenses.
To understand Mullins, we look first at limitations that courts had imposed previously on the applicability of antitrust defenses to contract suits. The leading pre Mullins case is Kelly v. Kosuga, 358 U.S. 516, 79 S.Ct. 429, 3 L.Ed.2d 475 (1959), which involved a suit by a seller of onions against a buyer for failure to pay. As a defense, the buyer, who, like the seller, was an onion supplier, alleged that he had been coerced to buy the onions by the seller’s threats to dump a large quantity on the market, thereby depressing prices. The contract-suit defendant agreed to buy 50 cars of onions, and both plaintiff and defendant agreed not to deliver any onions on the market for the remainder of that trading season, thereby artificially decreasing demand and inflating futures prices. The Court rejected the defendant’s argument that, because he was coerced into buying the onions by a threat of unlawful conduct, the contract was unenforceable. In doing so, it noted that “the plea of illegality based on violation of the Sherman Act has not met with much favor in this Court.” Id. at 518, 79 S.Ct. at 431. It then stated the following rule for deciding when to enforce illegal contracts:
Past the point where the judgment of the Court would itself be enforcing the precise conduct made unlawful by the [Sherman] Act, the courts are to be guided by the overriding general policy ... “of preventing people from getting other people’s property for nothing when they purport to be buying it.”
Id. at 520-21, 79 S.Ct. at 432 (quoting Continental Wall Paper Co. v. Louis Voight & Sons, Co., 212 U.S. 227, 271, 29 S.Ct. 280, 296, 53 L.Ed. 486 (1909) (Holmes, J., dissenting)).
Kosuga was generally viewed as permitting antitrust defenses in only a very narrow class of contract suits, courts being understandably hesitant to interpose complex antitrust issues in a simple suit for breach of contract. See Mullins, 642 F.2d at 1311 (D.C.Cir.1981), Viacom International, Inc. v. Tandem Productions, Inc., 526 F.2d 593 (2d Cir.1975). This court, in particular, read Kosuga to limit antitrust de[234]*234fenses to situations where the requested enforcement was of agreements not to compete or other direct market restrictions, that made “the court ... a party to an anticompetitive scheme.” Mullins, 642 F.2d at 1310 (quoting Kosuga, 358 U.S. at 520, 79 S.Ct. at 432); see also id. at 1311 n. 9.
This court’s decision in Mullins, however, was reversed by the Supreme Court. See 455 U.S. at 78-79, 102 S.Ct. at 857. In Mullins, the defendant, a coal producer, agreed to make contributions to United Mine Worker health and retirement funds based in part on the quantity of coal it purchased from non-union producers. The defendant failed to report such purchases and to make contributions based on them. After the contract expired, the union sued to collect the owed contributions. Clearly, enforcement of the promise to contribute to the welfare fund would not have directly impeded'competition at that point in time. See id. at 81 n. 6, 102 S.Ct. at 858 n. 6. Nonetheless, the Supreme Court allowed the asserted antitrust defense, stating:
If [defendant] Kaiser’s undertaking is illegal under the antitrust .. . laws, it is because of the financial burden which the agreement attached to purchases of coal from non-UMW producers, even though they may have contributed to other employee welfare funds. It is plain enough that to order Kaiser to pay would command conduct that assertedly renders the promise an illegal undertaking under the federal statutes.
Id. at 79, 102 S.Ct. at 857.
In so holding, however, the Court cited with favor language in Kosuga that lower courts had relied on to strictly limit applicability of antitrust defenses. See 455 U.S. at 80, 102 S.Ct. at 857 (“plea of illegality based on violation of the Sherman Act has not met with much favor”) (quoting Kosuga, 358 U.S. at 518, 79 S.Ct. at 431). In addition, Mullins accepted the Kosuga rationale that an antitrust defense to a contract suit may be raised only where enforcement “would make the courts a party to the carrying out of one of the very restraints forbidden by the Sherman Act.” Id. 455 U.S. at 81, 102 S.Ct. at 857 (quoting Kosuga, 358 U.S. at 520, 79 S.Ct. at 432). In Mullins, the promise to contribute to the health and retirement funds in proportion to defendant’s purchases of non-union coal was a means by which the plaintiff “enforced” restraints on purchases of non-union coal. By linking contributions to the purchase of non-union coal, this promise on its face embraced the very restraint of trade that the defendant alleged violated the Sherman Act. Had the Court assisted the uniori in collecting such contributions, it would have effectively become a party to the allegedly illegal scheme to discourage non-union coal purchases. Thus, in permitting the defendant to raise its antitrust defense in Mullins, the Court opened the window only a notch to antitrust defenses, i.e., it refused to enforce a promise to pay that was itself a mechanism to police anti-competitive conduct.
Unlike the “illegal promise” in Mullins, the promises to pay franchise fees in this case do not appear on their face to be primarily means to enforce the allegedly illegal tie-ins between the wax figures and start-up services. They appear rather to be a consideration for goods and services, to be paid for on an installment basis, i.e., a routine exchange which Mullins was careful to distinguish from the penalty-like agreement it refused to enforce. See Mullins, 455 U.S. at 80, 102 S.Ct. at 857 (antitrust defense disfavored in action to recover agreed price for goods sold). This is not a case where the appellants turned to an alternative supplier of start-up services and now object to paying a “penalty” for doing so.9 To transform the contracts here into illegal tie-ins would require complex proof of monopoly power in the tying market and leverage of [235]*235that power in the tied market. Even then, their vice would extend only to the amount that the agreed prices exceeded the fair value of the goods and services received and consumed—the portion of the prices that could be traced to the illegal practice. The complexity of proof and speculative nature of appellants’ defenses seem to us to place them outside of the Mullins exception and clearly within the ambit of disfavor for such defenses articulated in Kosuga. And even if there might be grounds for such a defense in other cases, we reject it here, where it was first raised ten years after the figures and the “tied” start-up services had been received and consumed without objection by the buyer.10 We therefore hold in the circumstances of this case that the obligation to make franchise payments persists and the defense that the original agreement included a tainted tie-in sale may not be raised. The remote danger, in a case such as this, that the court will be a party to enforcing an illegal restraint, seems far outweighed by the probability that allowing the defense would let the buyer escape from its side of a bargain long after it had secured exactly what it had bargained for, as well as involve the courts in a prolonged controversy over whether an illegal tie-in existed due to the seller’s market power and how that tie-in affected the agreed price for goods and services.
We also hold that appellants cannot raise any illegality that may attach to the Gatlinburg lease as a defense to appellees’ counterclaim for lease payments. Appellants nowhere attack their obligation to pay rent, standing alone, as illegal under the Sherman Act. Such a rationale would lead to the absurd result that all leases violate the antitrust laws. Instead, appellants allege that they were coerced to lease the figures as part of a scheme by appellees to perpetuate their monopoly over Lynch figures. But this allegation raises factual controversies, perhaps relevant to appellants’ contentions that the lease was part of a bigger scheme to monopolize the wax museum figure market, that are entirely unrelated to the contract claim before us. It is precisely this type of antitrust defense that Kosuga clearly held, and Mullins affirmed, to be inappropriate in a simple suit for the purchase price of delivered goods. See Mullins, 455 U.S. at 80, 102 S.Ct. at 457, Kosuga, 358 U.S. at 521, 79 S.Ct. at 432. In accord with these cases and the district court’s decision, we hold that Gatlinburg may not raise the alleged antitrust illegality of its lease of Lynch figures as a defense to appellees’ suit for rent.
IV. Relief Awarded for Appellees’ Counterclaims
We next consider appellants’ attack on the award of prejudgment interest and the order requiring them to make future franchise and lease payments as they come due. Although appellants’ obligations to pay franchise fees and rent under the Gettysburg and Gatlinburg agreements ended in 1982, Williamsburg’s obligation to pay 2%% of gross receipts runs in perpetuity.
We find no merit to appellants’ position on the issue of prejudgment interest. The district court properly followed the District of Columbia’s statutory prescription, which states:
In an action ... to recover a liquidated debt on which interest is payable by contract or by law or usage, the judgment for the plaintiff shall include interest on the principal debt from the time when it [236]*236was due and payable, at the rate fixed by the contract, if any, until paid.11
D.C.Code § 15-108 (1981).
We find more convincing appellants’ contentions that the district court did not properly justify granting injunctive relief requiring future payment of fees as they become due. The district court apparently did not consider the contract to have been terminated or repudiated.12 By requiring future payments, it essentially ordered appellants to continue performing their contractual obligations. The court thus denied the appellants any opportunity to repudiate the contract and thereby obligate appellees to mitigate damages flowing from any future breach. See Restatement (Second) of Contracts § 350.
The district court, however, entered its order before it determined that the appellees did not owe continuing operating services under the franchise agreements. Thus, after it entered its order, it may have concluded that appellees did not in fact owe anything more to appellants under the franchise agreements. In that case, appellants’ failure to pay the fees may have been a total breach. See id. § 243 (“Effect of a Breach by Non-Performance as Giving Rise To a Claim for Damages for Total Breach”). But, if that is the case, the damages flowing from the total breach should have been reduced to a sum certain, if possible. The only justification for ordering future payments as they become due would be a finding of total breach (after appellees performed their part of the contracts) and so great an uncertainty about the amount of damages (based on future gross receipts) that ordering future payments was necessary to ensure their accurate assessment. See id. §§ 359, 360 (specific performance justified where damages not provable with reasonable certainty). The court’s rationale is not sufficiently developed for us to determine if injunctive relief ordering payment of franchise fees as they become due is warranted under this theory. We remand to the district court for a determination of whether the breach was total or partial, and if total, whether the nature of the promised payments justifies its order of future payments.
V. Remaining Issues
We need not dwell long on the two remaining points on appeal—the disqualification of C & B and the district court’s order consolidating these three cases.
The appellants contend that the district court erred by not finding that C & B had represented Gettysburg in a matter “substantially related” to the franchise agreements at issue here. Brief for Appellants, at 28. The “substantial relation” test, which the district court properly invoked, was meant to protect an attorney’s former client from subsequent use of confidential disclosures by the attorney. See T.C. Theatre Corp. v. Warner Brothers Pictures, Inc., 113 F.Supp. 265, 268 (S.D.N.Y.1953). The court should not “inquire into the nature and extent” of any confidential disclosures. Id. Still, the party seeking disqualification has the burden of demonstrating a relationship between the matters in which counsel had represented him and those at issue which makes it reasonable to assume that some relevant confidential disclosures were made. See id. at 268; cf. Government of India v. Cook Industries, Inc., 569 F.2d 737, 739 (2d Cir.1978) (movant [237]*237must show matters are almost identical before court will disqualify counsel).
In this case, the district court allowed the appellants to develop a voluminous record on the extent of C & B’s representation of Gettysburg. It found that C & B did not represent Gettysburg on matters related to the franchise agreement. It further noted that C & B’s representation of Gettysburg was handled primarily through Dennis, who in addition to being owner of appellee Historic was then a coventurer in appellant, Gettysburg. Thus, it concluded that C & B was not in a position to receive information that Gettysburg intended to keep confidential vis-a-vis Historic. We do not think these factual findings are erroneous, much less clearly so. Cf. Allegaert v. Perot, 565 F.2d 246, 250 (2d Cir.1977) (holding “substantial relation” test not even implicated in such a situation).
Finally, the issue of whether these cases should not be consolidated because the antitrust issues are so complex that, at trial, a jury might be confused is mooted by our prior rulings.
Conclusion
For the reasons stated above, we affirm the district court’s grant of summary judgment for appellees on appellants’ tying claims, but vacate that grant on Gatlinburg’s monopolization claim stemming from its lease of Lynch figures and remand for further proceedings on that claim. We also affirm the grant of summary judgment for appellees on their contract claims for monies due under the franchise and lease agreements, but vacate the order that appellants pay future fees as they become due, remanding to the district court for reconsideration of that order. We affirm the district court on all other rulings.
It is so ordered.