Baxter International invented sevoflu-rane in the 1960s. This substance, a gas at room temperature, has good anesthetic properties. But it was too difficult and costly to produce commercially until the early 1980s, when Baxter devised an efficient process for its manufacture. Baxter obtained two process patents, the latter of which expires in December 2005. But the anesthetic gas still could not be sold in the United States unless it first received the fda’s approval, and Baxter was not willing to bear the costs of the required medical testing. So in 1988 it granted to Maruishi Pharmaceutical Company, of Japan, an exclusive worldwide license to practice the sevoflurane process patents Baxter owned or was pursuing. Maruishi obtained approval to sell the anesthetic in Japan, where it was a great success, as it has become in other nations since. This suggested that it would be worth obtaining the fda’s approval to sell in the United States. Abbott Laboratories took a subli-cense from Maruishi in 1992, obtained the fda’s approval after spending approximately $60 million on testing, and in 1995 began selling sevoflurane in the United States. Maruishi remains the sole manufacturer under the Baxter patents; Abbott resells sevoflurane that it purchases from Marui-shi, which pays Baxter a royalty based on its total sales. Today sevoflurane is the best-selling gas used for anesthesia in the United States, with approximately 58% of sales. Desflurane holds 35% of this market, and isoflurane accounts for almost all of the remaining sales. Isoflurane is not protected by any patent and sells for less, but it is slower in both onset and recovery and has an irritating taste and smell. Desflurane likewise has an annoying smell and aftertaste, though its properties otherwise are comparable to sevoflurane — which therefore has become the anesthetic of choice and commands a premium price.
Sevoflurane’s success gave rivals an incentive to invent around Baxter’s process patents. Ohio Medical Associates (now known as Ohmeda) set out in 1997 to do just this. In 1999 Ohmeda obtained a patent for a new way of making sevoflu-rane, distinct from Baxter’s process but equivalently cheap and effective. It planned to introduce a rival sevoflurane anesthetic, which it could do by filing a “me too” application with the fda. Ohmeda could receive approval without costly tests just by showing that the finished product is identical to Abbott’s.
Before Ohmeda could bring sevoflurane to market, it was acquired (in 1998) by Baxter — which decided to proceed with Ohmeda’s plans and compete with the se-voflurane made by Maruishi and sold in the United States by Abbott. Baxter concluded that it would make more from selling Ohmeda-process sevoflurane than it would lose in reduced royalties from Ma-ruishi for Baxter-process sevoflurane. *831Abbott, which contends that it has spent more than $1 billion to commercialize se-voflurane (including distribution of equipment for administering the drug and marketing to alert anesthesiologists to its benefits) did not welcome competition before the expiration of the Baxter patents. Abbott initiated arbitration under the Baxter-Maruishi agreement (to which it had become a party in 1992) and the Convention on the Recognition and Enforcement of Foreign Arbitral Awards, [1970] 21 U.S.T. 2517, T.I.A.S. No. 6997, implemented by 9 U.S.C. §§ 201-08. The agreement specifies a multi-national tribunal, which consisted of a U.S. attorney, a Spanish attorney, and a Japanese law professor.
Abbott contended that Baxter’s sale of Ohmeda-process sevoflurane before the Baxter patents expired would violate the exclusivity term of the license; Baxter replied, first, that the license does not explicitly forbid Baxter itself from competing with Maruishi (in other words, that exclusivity means only that Baxter can not issue any other licenses), and, second, that if the license does forbid Baxter from competing, then it violates U.S. antitrust law, particularly § 1 of the Sherman Act, 15 U.S.C. § 1, and is unenforceable. The arbitrators ruled against Baxter on both issues. The tribunal held that the license is exclusive in the strong sense and that any reduction in competition is attributable to Baxter’s decision to purchase the competing Ohme-da process while bound by this promise not to compete with its licensee. On cross suits filed by Abbott and Baxter, the district judge then directed Baxter to comply with the award, rejecting its contention that the license, as construed by the tribunal, violates the Sherman Act or the public policy of the United States. The judge observed that competition from desflurane, isoflurane, and sevoflurane made by any other process (for the sevoflurane molecule is unpatented) is unaffected. 2002 WL 467147, 2002 U.S. Dist. Lexis 5475 (N.D.Ill. Mar. 27, 2002).
Baxter argues at length in this court that the Baxter-Maruishi license, construed to keep Ohmeda-process sevoflurane off the U.S. market until 2006, is a territorial allocation unlawful per se under § 1 of the Sherman Act. But the initial question is whether Baxter is entitled to reargue an issue that was resolved by the arbitral tribunal. We think not; a mistake of law is not a ground on which to set aside an award. See George Watts & Son, Inc. v. Tiffany & Co., 248 F.3d 577 (7th Cir.2001). Section 207 says that “[t]he court shall confirm the award unless it finds one of the grounds for refusal or deferral of recognition or enforcement of the award specified in the said Convention.” Legal errors are not among the grounds that the Convention gives for refusing to enforce international awards. Under domestic law, as well as under the Convention, arbitrators “have completely free rein to decide the law as well as the facts and are not subject to appellate review.” Commonwealth Coatings Corp. v. Continental Casualty Co., 393 U.S. 145, 149, 89 S.Ct. 337, 21 L.Ed.2d 301 (1968). “Courts thus do not sit to hear claims of factual or legal error by an arbitrator”. United Paperworkers v. Misco, Inc., 484 U.S. 29, 38, 108 S.Ct. 364, 98 L.Ed.2d 286 (1987).
Arbitrators regularly handle claims under federal statutes. See, e.g., Rodriguez de Quijas v. Shearson/American Express, Inc., 490 U.S. 477, 109 S.Ct. 1917, 104 L.Ed.2d 526 (1989) (claims under the Securities Act of 1933); Shearson/American Express, Inc. v. McMahon, 482 U.S. 220, 107 S.Ct. 2332, 96 L.Ed.2d 185 (1987) (claims under the Securities Exchange Act of 1934 and the Racketeer Influenced and Corrupt Organizations Act); Scherk v. Alberto-Culver Co., 417 U.S. 506, 94 S.Ct. 2449, 41 L.Ed.2d 270 (1974) (international arbitration of claims under the Securities *832Exchange Act of 1934). We do not see any reason why things should be otherwise for antitrust issues — nor, more importantly, does the Supreme Court, which held in Mitsubishi Motors Corp. v. Soler Chrysler-Plymouth, Inc., 473 U.S. 614, 105 S.Ct. 3346, 87 L.Ed.2d 444 (1985), that international arbitration of antitrust disputes is appropriate.
Mitsubishi did not contemplate that, once arbitration was over, the federal courts would throw the result in the waste basket and litigate the antitrust issues anew. That would just be another way of saying that antitrust matters are not arbi-trable. Yet this is Baxter’s position. It wants us to disregard the panel’s award and make our own decision. The Supreme Court’s approach in Mitsubishi was different. It observed (473 U.S. at 639 n. 21, 105 S.Ct. 3346):
The utility of the Convention in promoting the process of international commercial arbitration depends upon the willingness of national courts to let go of matters they normally would think of as their own. Doubtless, Congress may specify categories of claims it wishes to reserve for decision by our own courts without contravening this Nation’s obligations under the Convention. But we decline to subvert the spirit of the United States’ accession to the Convention by recognizing subject-matter exceptions where Congress has not expressly directed the courts to do so.
Starting from scratch in court, as Baxter proposes, would subvert the promises the United States made by acceding to the Convention.
According to Baxter, there is a difference between arbitrating an antitrust issue (the subject of Mitsubishi) and creating one — which it accuses these arbitrators of doing. If the tribunal had construed the Baxter-Maruishi agreement differently, there would have been no antitrust problem. Baxter relies on the observation in George Watts that arbitrators are not allowed to command the parties to violate rules of positive law. That’s true enough, but whether the tribunal’s construction of the Baxter-Maruishi agreement has that effect was a question put to, and resolved by, the arbitrators. They answered no, and as between Baxter and Abbott their answer is conclusive. This is a point anticipated in Mitsubishi, which observed (id. at 638, 105 S.Ct. 3346): “While the efficacy of the arbitral process requires that substantive review at the award-enforcement stage remain minimal, it would not require intrusive inquiry to ascertain that the tribunal took cognizance of the antitrust claims and actually decided them.” The arbitral tribunal in this case “took cognizance of the antitrust claims and actually decided them.” Ensuring this is as far as our review legitimately goes.
Treating Baxter as bound (vis-a-vis Abbott) by the tribunal’s conclusion that the license (as construed to provide strong exclusivity) is lawful does not condemn the public to tolerate a monopoly. If the three-corner arrangement among Baxter, Maruishi, and Abbott really does offend the Sherman Act, then the United States, the FTC, or any purchaser of sevoflurane is free to sue and obtain relief. None of them would be bound by the award. As far as we can see, however, only Baxter is distressed by the award — and Baxter, as a producer, is a poor champion of consumers. See Atlantic Richfield Co. v. USA Petroleum Co., 495 U.S. 328, 110 S.Ct. 1884, 109 L.Ed.2d 333 (1990); Cargill, Inc. v. Monfort of Colorado, Inc., 479 U.S. 104, 107 S.Ct. 484, 93 L.Ed.2d 427 (1986); Brunswick Corp. v. Pueblo Bowl-O-Mat, Inc., 429 U.S. 477, 97 S.Ct. 690, 50 L.Ed.2d 701 (1977).
What relief the Antitrust Division, the ftc, or a consumer would obtain, if there is an antitrust problem, is an interesting *833question. Baxter thinks that the solution should be an order allowing it to sell Ohmeda-process sevoflurane. It wants to take its acquisition of Ohmeda as given and ask what consequences it has for exclusivity under the Baxter-Maruishi agreement. Yet this is anachronistic. The Baxter-Maruishi agreement came first, and its exclusivity rule was a lawful ancillary agreement designed to induce Maruishi and its sublicensees to make the investments needed to bring the new drug to market. See generally Polk Bros., Inc. v. Forest City Enterprises, Inc., 776 F.2d 185 (7th Cir.1985); Rothery Storage & Van Co. v. Atlas Van Lines, Inc., 792 F.2d 210 (D.C.Cir.1986) (Bork, J.). At the time Baxter acquired Ohmeda it was obliged by contract to refrain from producing sevoflu-rane until 2006. (This is how the tribunal understood the Baxter-Maruishi agreement, and a court must accept this interpretation.) So if there is an antitrust problem, it lies in the acquisition — and the remedy would be divestiture of the Ohme-da process patent. Baxter can achieve that outcome on its own. Baxter, which can solve unilaterally any antitrust problem, is in no position to insist that the burden of solution fall on Abbott by depriving it of the benefit of the exclusive Baxter-Maruishi license. Why should a decision Baxter made in 1998 reduce the rights Abbott enjoys under a promise Baxter made to Maruishi in 1988? But it is unnecessary to pursue this line of argument. All that matters today is that the arbitrators have concluded that the antitrust laws (and Baxter’s related arguments, which we need not address) do not diminish Abbott’s contractual rights — and that decision is conclusive between these parties.
Affirmed