This appeal from the dismissal of a suit seeking an order to arbitrate requires us to consider the intersection of class actions, arbitration, and Colorado River (parallel-proceeding) abstention. Underlying the appeal is a dispute between a group of affiliated corporations (CIGNA for short) and 288,000 (!) physicians, hospitals, and other providers of health care with which CIGNA, an administrator of employee health-benefits plans, has contracts for the provision of health care to the participants in the plans. Under these "managed care" contracts, as they are known, CIGNA reimburses its contract partners for the health-care services that they provide in fulfillment of its obligations to participants in the plans that it administers. The providers claim that after making these contracts CIGNA installed a computer program for calculating the amount it owed them that has resulted in systematic under-payment, in breach of their contracts.

In May 2000 the providers filed a class action in an Illinois state court against CIGNA which CIGNA wanted to but could not remove to federal court because one of the named plaintiffs was a citizen of Texas, as is one of the CIGNA affiliates named as defendants. However, many of the managed-care contracts contain an arbitration clause, and in July 2001, just days after the end of the period for providers to opt out if they wanted from the state court suit, CIGNA filed suit in federal district court against the named plaintiffs in the state court suit minus the Texas physician and the rest of the class. It based federal jurisdiction on diversity of citizenship and sought an order under section 4 of the Federal Arbitration Act (Title 9 of the U.S.Code) to compel arbitration of all disputes arising under managed-care contracts with members of the class that contain an arbitration clause. These are not all the disputes between CIGNA and the class. A number of the managed-care contracts (we don't know how many) do not contain an arbitration clause. But some or all of the providers that had such contracts may have received from CIGNA a document called "Program Requirements" that, CIGNA argues, grafted an arbitration clause onto the contract. Because the arbitrability of the disputes under these contracts would have to be determined on a contract-by-contract basis, CIGNA argues that the arbitrability of those disputes cannot be decided in a class action and so must be resolved by the state court. CIGNA's position is inconsistent, since the suit in the state court, the suit in which it concedes that the issue of the arbitrability of these other disputes must be resolved, is itself a class action. However that may be, a few days after filing its federal class action suit CIGNA moved the state court to order arbitration of the arbitrable disputes not encompassed by the federal suit.

In January 2002 the district judge dismissed the suit on the basis of the abstention doctrine created by Colorado River Water Conservation District v. United States, 424 U.S. 800, 818-20, 96 S. Ct. 1236, 47 L. Ed. 2d 483 (1976), precipitating this appeal. By this time, because the state court judge had refused to stay the proceedings before him pending the resolution of CIGNA's federal suit, CIGNA had produced hundreds of thousands of managed-care contracts in response to the providers' discovery requests and these contracts were being held in a document depository in Belleville, Illinois, the site of the state court. CIGNA was particularly disturbed by the state judge's refusal to stay discovery of the merits of the contract disputes; it argues that discovery with respect to any dispute that is arbitrable is the business of the arbitrators. But at least the state judge did say that he had not by denying the stay intended to prejudge the issue of arbitrability.

The providers' position on that issue is unclear, but clearly they are not yet prepared to concede that all their contractual disputes, or even all that arise out of managed-care contracts that contain an arbitration clause, are arbitrable. The issue of arbitrability is at present before the state judge with briefs due this month.

A federal court is authorized to stay proceedings in a lawsuit before it because parallel proceedings are pending in another court, either federal or state. Moses H. Cone Memorial Hospital v. Mercury Construction Corp., 460 U.S. 1, 19, 103 S. Ct. 927, 74 L. Ed. 2d 765 (1983); Will v. Calvert Fire Ins. Co., 437 U.S. 655, 662-63, 98 S. Ct. 2552, 57 L. Ed. 2d 504 (1978) (plurality opinion); Finova Capital Corp. v. Ryan Helicopters U.S.A., Inc., 180 F.3d 896, 898 (7th Cir.1999); Burns v. Watler, 931 F.2d 140, 145 (1st Cir.1991). It should not dismiss the proceedings before it, however. See Selmon v. Portsmouth Drive Condominium Ass'n, 89 F.3d 406, 409-10 (7th Cir.1996), and cases cited there. That would be illogical; the fact that a parallel case, especially one brought by the opposing party, is pending says nothing about the merits or propriety of the suit in the abstaining court. Logic aside, a stay "permits the federal court to retain jurisdiction in case the state court action does not meet its anticipated end. A stay has the additional advantage of bringing the case back before the same federal judge if a determination is needed as to the preclusive effects of the state judgment or decisions." Lumen Construction, Inc. v. Brant Construction Co., 780 F.2d 691, 698 (7th Cir.1985). In light of these considerations, the providers' counsel was right to concede at the argument of the appeal that the district judge's order should be reformed from a dismissal to a stay. Id.; LaDuke v. Burlington Northern R.R., 879 F.2d 1556, 1562 (7th Cir.1989); Attwood v. Mendocino Coast District Hospital, 886 F.2d 241, 245-46 (9th Cir.1989); see also Tice v. American Airlines, Inc., 288 F.3d 313, 318 (7th Cir.2002). We note parenthetically that had the district judge stayed the suit rather than dismissing it, we would still have had appellate jurisdiction because "a stay of the federal suit pending resolution of the state suit [would mean] that there would be no further litigation in the federal forum; the state court's judgment on the issue would be res judicata." Moses H. Cone Memorial Hospital v. Mercury Construction Corp., supra, 460 U.S. at 10; see also In re Kozeny, 236 F.3d 615, 618 (10th Cir.2000) (per curiam); Schall v. Joyce, 885 F.2d 101, 104-05 (3d Cir.1989); General Reinsurance Corp. v. Ciba-Geigy Corp., 853 F.2d 78, 80-81 (2d Cir.1988).

Abstention in favor of a parallel proceeding in another court is disfavored, because it deprives the plaintiff of his choice of forum in the likely event that, as just noted, the effect of abstention is to make the decision in the parallel proceeding res judicata in the proceeding that has been stayed. See also Evans Transportation Co. v. Scullin Steel Co., 693 F.2d 715, 718 (7th Cir.1982). But there is no hard and fast rule as to when parallel-proceeding abstention is proper or improper, Moses H. Cone Memorial Hospital v. Mercury Construction Corp., supra, 460 U.S. at 15, 103 S. Ct. 927, and the close relation between the decision to abstain and normal docket control (a district judge is routinely required to decide how fast to move particular cases along) makes it appropriate to give at least some weight to the judge's decision to abstain. Id. at 19, 103 S. Ct. 927; Will v. Calvert Fire Ins. Co., supra, 437 U.S. at 665, 98 S. Ct. 2552; Sverdrup Corp. v. Edwardsville Community Unit School District No. 7, 125 F.3d 546, 550 (7th Cir.1997); Burnett v. Physician's Online, Inc., 99 F.3d 72, 76 (2d Cir.1996).

CIGNA points out that no federal appellate court has ever upheld a decision to abstain in a suit seeking an order to compel arbitration. The reason may just be, however, that such decisions are rare. In re Mercury Construction Corp., 656 F.2d 933, 941 (4th Cir.1981) (en banc), aff'd. under the name Moses H. Cone Memorial Hospital v. Mercury Construction Corp., supra; Ferrari North America, Inc. v. Crown Auto Dealerships, No. 90-8541(KMW), 1995 WL 614558, *4 (S.D.N.Y. Oct. 19, 1995). Apart from a handful that have been reversed, we have found only five: Green Tree Financial Corp. v. Holt, 171 F.R.D. 313, 319 (N.D.Ala. 1997); Pepsico Inc. v. Oficina Central De Asesoria Y Ayuda Tecnica, C.A., 945 F. Supp. 69, 70, 71 (S.D.N.Y. 1996); Lexington Ins. Co. v. Reliance Ins. Co., Civ. A. No. 94-3642, 1995 WL 363744, at *1 (E.D.La. June 16, 1995); Gerling-Konzern Globale Rueckversicherungs-Ag v. Selcke, No. 93 C 4429, 1993 WL 443404, at *3 (N.D.Ill. Oct.29, 1993); E.C. Ernst, Inc. v. Potlatch Corp., 462 F. Supp. 694, 700-01 (S.D.N.Y.1978). It is not as if any appellate court had held that abstention is never appropriate in a suit to compel arbitration. None has. CIGNA cites We Care Hair Development, Inc. v. Engen, 180 F.3d 838 (7th Cir.1999), a case much like this, it is true — except that there was no issue of abstention. The only issue was whether the federal court had jurisdiction to compel arbitration notwithstanding the parallel proceeding in the state court. We held that it did, but this holding obviously would not have precluded abstention, which presupposes jurisdiction, had abstention been sought. In Bio-Analytical Services, Inc. v. Edgewater Hospital, Inc., 565 F.2d 450, 454 and n. 5 (7th Cir.1977), we explicitly left open the issue presented by this appeal.

CIGNA's principal argument against abstention, as distinct from its futile invocation of inapposite authority, is that the providers' state court suit was an effort to derail its contractual right to arbitration. It points out that "federal courts will not `permit a party to a contract to circumvent an arbitration clause by commencing litigation in a state court.'" In re Mercury Construction Corp., supra, 656 F.2d at 941. But what exactly is "circumvention" in this context? The right to arbitrate arguably conferred by the parties' contract may be contested. The providers had a perfect right to sue for breach of contract. The arbitration clause is a defense to the further prosecution of the suit in court that CIGNA was entitled to raise in the state court proceeding and has raised there. And who is derailing whom? By leaving out the non-diverse named plaintiff in its suit to compel arbitration, CIGNA attempted to deprive the state court of its opportunity to order arbitration of those disputes with the providers that arise out of contracts containing explicit arbitration clauses.

The arbitration clauses do more than provide a potential defense, however. Because CIGNA can satisfy the requirements for diversity jurisdiction with respect to a suit against the named plaintiffs (minus the Texan) and the rest of the class, it was entitled to bring this suit for an order under 9 U.S.C. § 4 to compel arbitration. (And if CIGNA was playing games in not naming the Texan, the class lawyers in the state suit may have been playing games in naming him, in order to prevent removal to federal court.) If, however, CIGNA is seeking relief equally available from the state court, the district court had compelling reasons of judicial economy to abstain, because the procedure favored by CIGNA involves an awkward split of the issue of arbitrability between contracts that contain an arbitration clause and contracts claimed to incorporate such a clause by reference in another document, and also because while the issue of arbitrability is about to be briefed in the state court there has been no movement in CIGNA's federal suit. There hasn't even been a determination that the suit can be maintained as a class action — and suits against defendant classes, though authorized, Fed.R.Civ.P. 23(a) (a class may "sue or be sued"); Kaucky v. Southwest Airlines Co., 109 F.3d 349, 350 (7th Cir.1997); Consolidated Rail Corp. v. Town of Hyde Park, 47 F.3d 473, 483 (2d Cir.1995); 7A Charles Alan Wright, Arthur R. Miller & Mary Kay Kane, Federal Practice and Procedure § 1770, p. 395 (2d ed.1986), are rare birds. We have called them "exceptional," Channell v. Citicorp National Services, Inc., 89 F.3d 379, 387 (7th Cir.1996), and Professor Coffee has with harmless exaggeration called them "as rare as unicorns." John C. Coffee, Jr., "Class Action Accountability: Reconciling Exit, Voice, and Loyalty in Representative Litigation, 100 Colum. L.Rev. 370, 388 (2000); see also Thomas E. Willging et al., "An Empirical Analysis of Rule 23 to Address the Rule-making Challenges," 71 N.Y.U.L.Rev. 74, 119-20 (1996). So a lively passage of arms can be anticipated in the district court (should we reverse) over whether treating CIGNA's suit as a class action would be appropriate.

The arbitration clause incorporated by reference (if it is incorporated by reference and thus made applicable to disputes arising under the contracts that do not contain an arbitration clause) may, for all we know, be identical to the clause contained in the contracts, and that would mean that two judges, one state and one federal, would be addressing the identical issue. And given the state court's head start, the state proceeding would probably wind up before the federal and preclusion would attach, and then CIGNA would have gained nothing but delay from its maneuvers. Delay may be what it wants; sufficient unto the day is the evil thereof.

For all these reasons, we do not think the case governed by the refusal of the Supreme Court in Dean Witter Reynolds Inc. v. Byrd, 470 U.S. 213, 221, 105 S. Ct. 1238, 84 L. Ed. 2d 158 (1985), to be "persuaded by the argument that the conflict between two goals of the [Federal] Arbitration Act — enforcement of private agreements and encouragement of efficient and speedy dispute resolution — must be resolved in favor of the latter in order to realize the intent of the drafters." The Court explained that "the preeminent concern of Congress in passing the Act was to enforce private agreements into which parties had entered, and that concern requires that we rigorously enforce agreements to arbitrate, even if the result is `piecemeal' litigation, at least absent a countervailing policy manifested in another federal statute. By compelling arbitration of state-law claims, a district court successfully protects the contractual rights of the parties and their rights under the Arbitration Act." To the same effect see Moses H. Cone Memorial Hospital v. Mercury Construction Corp., supra, 460 U.S. at 20. The issue in Dean Witter was whether arbitration of pendent state-law claims should be deferred to allow the district court to decide the main, federal claim, assumed to be nonarbitrable; it was not whether a state or a federal court should decide whether the pendent claims were arbitrable. The choice is not, not yet any-way, between judicial and arbitral resolution of the parties' dispute.

Granted, there is more to the Federal Arbitration Act than the creation of a remedy in federal district courts for breach of a contractual undertaking to arbitrate a dispute. With regard to contracts in interstate commerce, which CIGNA's managedcare contracts are acknowledged to be, the Act makes arbitration clauses "valid, irrevocable, and enforceable, save upon such grounds as exist at law or in equity for the revocation of any contract." 9 U.S.C. § 2. This provision forbids a state to discriminate against arbitration clauses; the state must give them the same respect it gives ordinary contracts. Doctor's Associates, Inc. v. Casarotto, 517 U.S. 681, 687, 116 S. Ct. 1652, 134 L. Ed. 2d 902 (1996); Koveleskie v. SBC Capital Markets, Inc., 167 F.3d 361, 367 (7th Cir.1999); S + L + H S.p.A. v. Miller-St. Nazianz, Inc., 988 F.2d 1518, 1526-27 (7th Cir.1993); Circuit City Stores, Inc. v. Adams, 279 F.3d 889, 892 (9th Cir.2002); PaineWebber Inc. v. Elahi, 87 F.3d 589, 593 (1st Cir.1996); W.M. Schlosser Co. v. School Bd. of Fair-fax County, 980 F.2d 253, 258-59 (4th Cir. 1993). It goes even further: it requires both federal and state courts to apply a federal common law of arbitrability to the arbitration of disputes arising under contracts in commerce, a common law applicable equally in federal and state courts, Allied-Bruce Terminix Companies, Inc. v. Dobson, 513 U.S. 265, 272, 115 S. Ct. 834, 130 L. Ed. 2d 753 (1995); Southland Corp. v. Keating, 465 U.S. 1, 14-15, 104 S. Ct. 852, 79 L. Ed. 2d 1 (1984); Circuit City Stores, Inc. v. Adams, supra, 279 F.3d at 892-as the Illinois courts, which have, incidentally, said they favor arbitration as a method of dispute resolution, e.g., Board of Managers of Courtyards at Woodlands Condominium Ass'n v. IKO Chicago, Inc., 183 Ill. 2d 66, 231 Ill. Dec. 942, 697 N.E.2d 727, 730 (Ill.1998); United Cable Television Corp. v. Northwest Illinois Cable Corp., 128 Ill. 2d 301, 131 Ill. Dec. 172, 538 N.E.2d 547, 549 (Ill.1989), acknowledge. Caligiuri v. First Colony Life Ins. Co., 318 Ill.App.3d 793, 252 Ill. Dec. 212, 742 N.E.2d 750, 755 (Ill.App.2000); Caudle v. Sears, Roebuck & Co., 245 Ill.App.3d 959, 185 Ill. Dec. 627, 614 N.E.2d 1312, 1316-17 (Ill. App.1993); Konewko v. Kidder, Peabody & Co., 173 Ill.App.3d 939, 123 Ill. Dec. 617, 528 N.E.2d 1, 3 (Ill.App.1988).

CIGNA has one good point: the state judge's refusal to stay discovery on the merits of the providers' breach of contract claims until the issue of arbitrability is resolved puts the cart before the horse. If a dispute is arbitrable, responsibility for the conduct of discovery lies with the arbitrators — indeed, for the sake of economy and in contrast to the practice in adjudication, parties to an arbitration do not conduct discovery; the arbitrators do. 9 U.S.C. § 7; Amgen, Inc. v. Kidney Center of Delaware County, Ltd., 95 F.3d 562, 563 (7th Cir.1996); National Broadcasting Co. v. Bear Stearns & Co., 165 F.3d 184, 190-91 (2d Cir.1999); Burton v. Bush, 614 F.2d 389, 390 (4th Cir.1980); cf. Olympia & York Florida Equity Corp. v. Gould, 776 F.2d 42, 43 (2d Cir.1985) (per curiam); Yeargin Construction Co. v. Parsons & Whittemore Alabama Machinery & Services Corp., 609 F.2d 829, 831 (5th Cir. 1980) (per curiam). That is water over the dam, however. As far as we can tell, discovery relating to the state court judge's resolution of the issue of arbitrability is complete, so that the only question for us today is whether he will conscientiously and sensibly apply the proper legal standard to the issue of arbitrability. We are not certain that he will; his actions in certifying a class even though many of its members were basing their claims on contracts containing arbitration clauses, in allowing discovery on the merits to proceed before ruling on arbitrability, and in delaying as long he has ruling on that question (CIGNA moved the state judge for an order to arbitrate in July 2001, almost a year ago), do make us wonder whether federal arbitration rights may not be a second-order concern for him. But our doubts don't rise to the level at which we could deem the district judge's action in abstaining an abuse of discretion. Although CIGNA is not an Illinois company, neither are most of the members of the class, which is nationwide, so bias in favor of state residents should not be operative. We rather doubt that the state judge is eager to adjudicate disputes among almost 300,000 parties if the laborious task of dispute resolution can be shifted to the backs of arbitrators.

This is all speculation; it is enough that we emphasize — and we do emphasize — that if down the road the state court judge proves unwilling or unable to enforce CIGNA's valid rights if any to arbitration and CIGNA cannot get prompt relief from the state appellate courts, it can ask the district judge to lift the stay; and under the posited conditions, which were not the conditions when he ruled, CIGNA would receive a sympathetic hearing. But for now we think it best (more precisely, we think the district judge did not abuse his discretion in thinking it best) to allow the federal suit to be stayed at least until the state judge rules on CIGNA's motion to compel arbitration — provided that ruling is not too long delayed. Nor would that ruling necessarily preclude further proceedings in the district court, for in the "event that the state court action proves inadequate to protect the parties' federal rights, ordinary principles of res judicata and collateral estoppel would not prevent them from bringing their claims back before a federal court. `Redetermination of issues is warranted if there is reason to doubt the quality, extensiveness, or fairness of procedures followed in prior litigation.'" Lumen Construction, Inc. v. Brant Construction Co., supra, 780 F.2d at 697 (citation omitted), quoting Montana v. United States, 440 U.S. 147, 164 n. 11, 99 S. Ct. 970, 59 L. Ed. 2d 210 (1979). It is true that the preclusive effect of a state court judgment in a federal case is a matter of state rather than of federal law, Marrese v. American Academy of Orthopaedic Surgeons, 470 U.S. 373, 380-81, 105 S. Ct. 1327, 84 L. Ed. 2d 274 (1985), as may not have been clear when Lumen was decided; but, consistent with Lumen and with Montana v. United States, Illinois law denies collateral estoppel effect to a finding not made on the basis of a fair and adequate hearing. E.g., Fried v. Polk Bros., Inc., 190 Ill.App.3d 871, 138 Ill. Dec. 105, 546 N.E.2d 1160, 1164 (Ill.App.1989); Coronet Ins. Co. v. Booker, 158 Ill.App.3d 466, 110 Ill. Dec. 616, 511 N.E.2d 793, 796-97 (Ill. App.1987).

The judgment is modified to convert dismissal of the suit into a stay of the suit and so modified is

AFFIRMED.