POSNER, Circuit Judge.

We have consolidated the motions to dismiss these two appeals for lack of appellate jurisdiction in order to address recurrent issues of appealability that are a source of understandable confusion to the bar. In No. 83-2910, the plaintiff sued a brokerage house and others. She alleged "churning" and other violations of federal securities law, and joined pendent claims under state law. The defendants moved the district court for an order compelling arbitration of the pendent claims but staying the arbitration until the court disposed of the plaintiff's federal claims. The court ordered arbitration but refused to stay its order, and the defendants have appealed, complaining about the refusal to stay. In No. 83-3310, a union sued a company under section 301 of the Taft-Hartley Act, 29 U.S.C. § 185, for breach of a collective bargaining agreement. In count I the plaintiff asked for an order compelling arbitration, and in count II for equitable and other relief. The court ordered arbitration and stayed proceedings on count II, and the defendant has appealed from both the order to arbitrate and the stay of further proceedings in the district court on count II.

As a general rule, only a district court's final decisions are appealable to a court of appeals. See 28 U.S.C. § 1291. The orders that are sought to be appealed here are not final in the sense of concluding the litigation in the district court. Nevertheless, if a district court, when ordering arbitration, retains jurisdiction for the sole and limited purpose of enforcing any award that the arbitrators may make, the order to arbitrate is sufficiently final to be immediately appealable. University Life Ins. Co. of America v. Unimarc Ltd., 699 F.2d 846, 848-50 (7th Cir. 1983). But neither of the present appeals is from an order that is final in this sense. In No. 83-2910 the order to arbitrate is limited to the pendent claims. The other claims may not even be arbitrable, and in any event they have been retained for trial in the district court, as in Whyte v. THinc Consulting Group Int'l, 659 F.2d 817, 818 (7th Cir. 1981). See also Matterhorn, Inc. v. NCR Corp., 727 F.2d 629, 631-632 (7th Cir. 1984); Hartford Financial Systems, Inc. v. Florida Software Services, Inc., 712 F.2d 724, 728-29 (1st Cir. 1983); University Life Ins. Co. of America v. Unimarc Ltd., supra, 699 F.2d at 848. Moreover, the appellants in No. 83-2910 are not complaining about the order to arbitrate — they sought it — but about the refusal to stay that order.

In No. 83-3310 the order to arbitrate was limited to count I of the complaint. Count II remains pending in the district court. The appellant describes count II as asking merely for contingent relief should the plaintiff's request for arbitration (count I) be denied. If this description were accurate, it would mean that by ordering arbitration the district court has mooted count II and left nothing pending in that court; but it is not accurate. Among the questions that the arbitrators have been asked to decide is the arbitrability of certain issues between the parties; and if the arbitrators decide that any of those issues are not arbitrable, proceedings under count II will become necessary. This is not so remote a contingency as to warrant a conclusion that by ordering arbitration the district court has terminated the proceeding before it other than to retain jurisdiction (as in University Life) to enforce the arbitrators' award.

An alternative basis for these appeals must be considered, however. 28 U.S.C. § 1292(a)(1) authorizes the immediate appeal of orders granting or denying preliminary injunctions, and under the Enelow-Ettelson doctrine, discussed recently in Rohrer, Hibler Replogue, Inc. v. Perkins, 728 F.2d 860, 863 (7th Cir. 1984) (per curiam); Matterhorn, Inc. v. NCR Corp., supra, and Medtronic, Inc. v. Intermedics, Inc., 725 F.2d 440 (7th Cir. 1984), an equitable stay of an action at law is appealable as a preliminary injunction. Now clearly the Enelow-Ettelson doctrine does not authorize the appeal in No. 83-3310. Count II, proceedings on which have been stayed pending the arbitrators' determination, asks for equitable as well as legal relief; and we have just held (in Medtronic) that a mixed law-equity action is equitable rather than legal for purposes of applying the Enelow-Ettelson doctrine, provided that the equitable relief sought is not merely incidental to the legal relief sought. See also Hartford Financial Systems, Inc. v. Florida Software Services, Inc., supra, 712 F.2d at 727. It is not merely incidental in this case; among other things, count II seeks an order of specific performance of the contract in suit, and such an order, if issued, would be more than incidental to any damages awarded for violation of the contract in the past. Since the underlying action thus is equitable for purposes of applying the Enelow-Ettelson doctrine, the stay of the action is not appealable under that doctrine.

The order in No. 83-2910 presents a more difficult Enelow-Ettelson question. It can be argued that whatever the nature of the underlying suit (it happens to be legal, an action for damages, rather than equitable), a stay of arbitration — a stay not of proceedings in the court issuing the stay but in another tribunal — is a classic injunction (misnamed a stay), and therefore the grant or denial of such a "stay" must be appealable under section 1292(a)(1). A. E. Plastik Pak Co. v. Monsanto Co., 396 F.2d 710, 713 (9th Cir. 1968). In Lummus Co. v. Commonwealth Oil Refining Co., 297 F.2d 80, 85-86 (2d Cir. 1961), however, the Second Circuit, in an opinion by Judge Friendly, rejected this approach entirely and held that such an order, whether granting or refusing a stay of arbitration, is not appealable as an injunction. This conclusion was based in part on the practical ground that allowing orders refusing stays of arbitration to be appealed immediately might impair one of the major advantages claimed for arbitration — its speed (see id. at 86). Although there is much force to Judge Friendly's approach, it has not been followed in any other circuit, see, e.g., Buffler v. Electronic Computer Programming Institute, Inc., 466 F.2d 694, 698-99 (6th Cir. 1972), including our own, which has twice held orders granting stays of arbitration to be immediately appealable. See Alberto-Culver Co. v. Scherk, 484 F.2d 611, 614 (7th Cir. 1973), rev'd on other grounds, 417 U.S. 506, 94 S.Ct. 2449, 41 L.Ed.2d 270 (1974), and Weissbuch v. Merrill Lynch, Pierce, Fenner Smith, Inc., 558 F.2d 831, 833 (7th Cir. 1977). Although Alberto-Culver is (tenuously) distinguishable from the present cases because the district judge not only issued a stay but explicitly enjoined the arbitration — tenuously because the precise form of the order should not matter, but its consequences — Weissbuch is not. ( Weissbuch, incidentally, characterizes Alberto-Culver as a stay case.) There are similar holdings in other circuits. Besides Buffler, see, e.g., Texaco, Inc. v. American Trading Transport. Co., 644 F.2d 1152, 1153-54 (5th Cir. 1981).

We are free, however, to hold that an order refusing, as opposed to an order granting, a stay of arbitration is not appealable under section 1292(a)(1). The circuits that have addressed the question have divided, roughly evenly; ours has not yet spoken. (Decisions rejecting appealability are Mellon Bank, N.A. v. Pritchard-Keang Nam Corp., 651 F.2d 1244, 1250 (8th Cir. 1981); Stateside Machinery Co. v. Alperin, 526 F.2d 480, 482-83 (3d Cir. 1975); New England Power Co. v. Asiatic Petroleum Corp., 456 F.2d 183, 186-87 (1st Cir. 1972), and, as a correlate to the Lummus doctrine, Greater Continental Corp. v. Schechter, 422 F.2d 1100, 1102-03 (2d Cir. 1970). Upholding appealability are Pitney Bowes, Inc. v. Mestre, 701 F.2d 1365, 1373 n. 14 (11th Cir. 1983); Petroleum Helicopters, Inc. v. Boeing-Vertol Co., 606 F.2d 114 (5th Cir. 1979) (per curiam), and A. E. Plastik Pak Co. v. Monsanto Co., supra, 396 F.2d at 713, though only the last actually discusses the issue.) The courts that refuse to distinguish between granting and refusing a stay of arbitration note that the distinction is difficult to square with the language of section 1292(a)(1), which allows appeals indifferently from orders denying as well as granting injunctions. The distinction can be supported, however, by reference to the concern expressed by Judge Friendly in Lummus with preventing delays in arbitration. If a stay of arbitration is granted, the arbitration is halted, and an immediate appeal, if it leads to reversal of the stay, may actually expedite the arbitration. But if refusals to stay arbitration are appealable, then anyone who wants to appeal from an order to arbitrate need only ask for a stay of the order; the denial of this request would be appealable; and the appellant would have a shot at persuading the district court or the court of appeals to stay the arbitration pending appeal. Even if one assumes that such stays would rarely be granted, and ignores the burden on the party seeking arbitration of having to fend off an interlocutory appeal while the arbitration is in progress — of having in other words to be active in two tribunals at once — allowing such an appeal would be inconsistent with decisions such as Whyte in this circuit which hold that orders to arbitrate that do not wind up the proceedings in the district court are not immediately appealable. For these reasons we join the circuits that hold that refusals to stay arbitration are not appealable under section 1292(a)(1). See also Note, Interlocutory Appeal of Orders Granting or Denying Stays of Arbitration, 80 Mich.L.Rev. 153 (1981).

We consider finally the argument in both cases that if arbitration is allowed to go forward before any nonarbitrable issues are determined by the district court, the appellants will be deprived, by operation of the doctrine of collateral estoppel, of their Seventh Amendment right to a jury trial of those issues, and that either mandamus or the collateral-order doctrine of Cohen v. Beneficial Industrial Loan Corp., 337 U.S. 541, 546, 69 S.Ct. 1221, 1225, 93 L.Ed. 1528 (1949), should be summoned to allow an immediate appeal that will ward off this consequence. But this argument confuses the merits of an appeal with the issue of appealability. If the district court erroneously ordered arbitration, the error can be corrected on appeal from any final order of the district court confirming the arbitration award or otherwise disposing of the litigation. If the appellants' argument prevailed, every order to arbitrate would be immediately appealable, contrary to Whyte and many other cases. True, there is authority that the erroneous denial of a demand for a jury trial can be corrected immediately by asking for a writ of mandamus under the All Writs Act, 28 U.S.C. § 1651(a), even if (what defeats most efforts to get mandamus) the petitioner's right is not indisputable. See 16 Wright, Miller, Cooper Gressman, Federal Practice and Procedure § 3935 at p. 243 (1977). But this principle has not been pushed so relentlessly as to allow an immediate appeal from every type of order that might result in a party's right to a jury trial being diminished by operation of res judicata or collateral estoppel. Applied to refusals to stay arbitration, the principle would let in by the back door what we have said we are unwilling to let in by the front door: immediate appeals of such refusals. We therefore join the First Circuit in refusing to allow mandamus to be used for this purpose. See USM Corp. v. GKN Fasteners, Ltd., 574 F.2d 17, 23 (1st Cir. 1978).

The appeals are dismissed for lack of jurisdiction in this court. The appellant's motion for a stay of the district court's order to arbitrate in No. 83-3310 pending review by this court is dismissed as moot. No costs in this court.

APPEALS DISMISSED.