opinion: PATRICK E. HIGGINBOTHAM, Circuit Judge:
  At the outset of this appeal from a stay of proceedings pending arbitration we face the question of our jurisdiction. Persuaded that because the sole claim was for specific performance the stay was not appealable as an injunctive order under 28 U.S.C. § 1292(a)(1), and that the trial judge’s finding of a contract between the two parties was not an appealable Cohen order, we dismiss for want of appellate jurisdiction.
  Oasis Oil & Refining Corp. sued Armada Transport & Refining Co. in the state district court of Texas seeking only specific performance of a contract for the sale of crude oil. ATR removed the state suit and the next day Oasis moved for a preliminary injunction compelling specific performance. Five days later on the morning of the hearing on the requested injunction and immediately before the taking of testimony, ATR filed its “Original Answer and Demand for a Jury Trial.” That Answer denied there was a contract and alternatively plead that if a contract be found further proceedings should be stayed pending arbitration. The district court denied Oasis’ application for a preliminary injunction. Then, after stating “it currently appears that the parties have indeed entered into a binding contract” containing an arbitration agreement, it granted the request for a stay of further proceedings pending arbitration. The district court denied ATR’s motion for reconsideration of the order. The motion urged that the court should have only decided whether Oasis was entitled to a preliminary injunction, in that the court’s ruling on the contract deprived ATR of a jury trial on the question of whether a contract existed. ATR here repeats its jury denial argument, and adds that the trial judge improperly consolidated the trial on the merits with the preliminary injunction hearing.
  Our jurisdiction is limited by the Enelow-Ettelson rule governing the appeal-ability of stay orders under 28 U.S.C. § 1292(a)(1). See Baltimore Contractors v. Bodinger, 348 U.S. 176, 75 S.Ct. 249, 99 L.Ed. 233 (1955); Ettelson v. Metropolitan Insurance Co., 317 U.S. 188, 63 S.Ct. 163, 87 L.Ed. 176 (1942); Enelow v. New York Life Insurance Co., 293 U.S. 379, 55 S.Ct. 310, 79 L.Ed. 440 (1935). We stated the rule in Jackson Brewing Co. v. Clarke, 303 F.2d 844, 845 (5th Cir.1962) (emphasis in original):
  [A]n order staying or refusing to stay proceedings in the district court is appeal-able under 1292(a)(1) only if (A) the action in which the order was made is an action which before the fusion of law and equity, was by its nature an action at law; and (B) the stay was sought to permit the prior determination of some equitable defense or counterclaim.
  In characterizing an action we adhere to the rule “that the equitable element must be more than ‘merely incidental’ if the element is to defeat an interlocutory appeal [citations omitted].” Thompson v. House of Nine, Inc., 482 F.2d 888 (5th Cir.1973). The sole relief sought by Oasis was of an equitable nature. Oasis sought no more than an order compelling specific performance. The Enelow-Ettelson rule is based on the idea that a modern court’s stay of a legal, but not equitable, action is analogous to an old equity court’s enjoining of proceedings in the law courts. See Baltimore Contractors v. Bodinger, 348 U.S. at 184-85, 75 S.Ct. at 254-255. That Oasis seems to have had an adequate damage remedy and his claim was therefore a likely loser is not enough for us to visualize this equitable claim as having been brought in the law courts. See USM Corp. v. GKN Fasteners, Ltd., 574 F.2d 17, 23 (1st Cir.1978). Although in this day of unitary actions, courts and commentators criticize as artificial the Enelow-Ettelson distinction between stays of legal and equitable actions, see C. Wright and A. Miller, 16 Federal Practice and Procedure § 3923, at 53, 53 n. 14 (1977), we are bound by the rule. We lack jurisdiction under 28 U.S.C. § 1292(a)(1) to review the order staying the proceedings pending arbitration.
  Nor can we agree with ATR that, because its quarrel is with the finding of the district court that a contract had been formed, that order is appealable under the doctrine of Cohen v. Beneficial Loan Co., 337 U.S. 541, 69 S.Ct. 1221, 93 L.Ed. 1528 (1949). Cohen created a “small class of decisions excepted from the final-judgment rule”; to come within this exception “the order must conclusively determine the disputed question, resolve an important issue completely separate from the merits of this action, and be effectively unreviewable on appeal from a final judgment.” Coopers and Lybrand v. Livesay, 437 U.S. 463, 468, 98 S.Ct. 2454, 2458, 57 L.Ed.2d 351 (1978). We have “repeatedly stressed the extraordinarily limited nature of the collateral order doctrine.” Anchor Hocking v. Willamette Industries, Inc., 694 F.2d 1041, 1042-43 (5th Cir.1983) (“We must therefore be parsimonious in our analysis of appealability and not grant an exception to the final-judgment rule unless ... all three requirements of Cohen are met.”)
  Here the determination that a contract existed is effectively reviewable on appeal from final judgment. On appeal from final judgment confirming or refusing to vacate the arbitration award, ATR may raise both the contract issue and its contention that the district court improperly consolidated the trial on the merits with the preliminary injunction hearing.
  ATR argues it was denied a right to try the contract issue to a jury before the trial court ruled on the motion for a stay, and that this denial ought to be weighed in the Cohen inquiry. Assuming its relevance we find no right to a jury trial here. ATR had no constitutional right to a jury trial, the action being solely equitable, as is the motion for a stay pending arbitration. See Shanferoke Coal & Supply Co. v. Westchester Serv. Corp., 293 U.S. 449, 55 S.Ct. 313, 79 L.Ed. 583 (1935).
  Nor did ATR have a right to a jury trial under the Federal Arbitration Act. Under ATR’s demand, the Federal Arbitration Act was triggered only if, and after, a contract was found. Thus no right under the Federal Arbitration Act to a jury trial on the contract issue was implicated.
  While it obtains the procedural relief it wanted ATR will suffer the delay and expense of an arbitration proceeding under a contract it may later prove was never formed. This sort of injury is inherent in orders staying proceedings pending arbitration and does not justify an exception to the final judgment rule. See USM Corp. v. GKN Fasteners, Ltd., 574 F.2d at 20. This dispute is indistinguishable from many if not most cases when proceedings are stayed pending arbitration. A Cohen exception here would tend to swallow the Enelow-Ettelson rule. Finding stay orders to be appealable under Cohen when the existence of a contract is disputed would be contrary to our long precedent that indexes appealability by categorization into legal and equitable claims.
  Finding no jurisdiction, we cannot proceed. Appeal DISMISSED.