KEARSE, Circuit Judge:

Defendant Connecticut National Bank ("Bank") appeals from an order of the United States District Court for the District of Connecticut, Peter C. Dorsey, Judge, affirming an order of the bankruptcy court which denied the Bank's motion to strike the jury trial demand of plaintiff Thomas M. Germain, Trustee for the Estate of O'Sullivan's Fuel Oil Co., Inc. ("O'Sullivan"). 112 B.R. 57. On appeal, the Bank contends that, for several reasons, the Trustee has no right to a jury trial under the Seventh Amendment to the Constitution. For the reasons below, we dismiss the appeal for lack of appellate jurisdiction.

I. BACKGROUND

O'Sullivan is the debtor in a liquidation proceeding under Chapter 7 of the Bankruptcy Code; the proceeding was converted to one under Chapter 7 after O'Sullivan had initially filed a voluntary petition for reorganization under Chapter 11. During the Chapter 11 phase, O'Sullivan was debtor-in-possession; the Bank was a postpetition lender. In connection with the conversion to Chapter 7, Germain was appointed Trustee.

The present action was commenced by the Trustee in a Connecticut state court to recover damages from the Bank on behalf of O'Sullivan for alleged wrongs to O'Sullivan while it was a debtor-in-possession. The Bank eventually removed the action to bankruptcy court. In that court, the Trustee filed a demand for jury trial; the Bank moved to strike the demand. The bankruptcy court denied the motion to strike. The district court upheld the denial and certified the question for immediate appeal to this Court pursuant to 28 U.S.C. § 1292(b) (1988). This Court, however, refused to grant leave to appeal, see id., ruling that such an interlocutory appeal is unauthorized by the Bankruptcy Code. See Germain v. The Connecticut National Bank, 926 F.2d 191 (2d Cir. 1991).

Concurrently with that attempt to obtain leave to appeal, the Bank filed the present appeal, contending that the district court's order upholding the bankruptcy court's refusal to strike the jury demand is a final collateral order that the Bank may appeal as of right under 28 U.S.C. § 1291 (1988) pursuant to the Cohen doctrine, see Cohen v. Beneficial Industrial Loan Corp., 337 U.S. 541, 69 S.Ct. 1221, 93 L.Ed. 1528 (1949). Though the Trustee has not questioned our jurisdiction to hear the appeal on this basis, we raise the question sua sponte, as we must, see Louisville Nashville Railroad v. Mottley, 211 U.S. 149, 152, 29 S.Ct. 42, 43, 53 L.Ed. 126 (1908). For the reasons below, we conclude that the Cohen doctrine is not applicable and that we therefore have no jurisdiction to entertain this appeal.

II. DISCUSSION

Section 1291 gives the courts of appeals jurisdiction to review "final decisions" of the district courts. 28 U.S.C. § 1291. An order denying a motion to strike a demand for jury trial is obviously not a final decision that disposes of the case. See City of Morgantown v. Royal Insurance Co., 337 U.S. 254, 256-59, 69 S.Ct. 1067, 1068-70, 93 L.Ed. 1347 (1949). The collateral order doctrine, on which the Bank relies, is a judicially created exception to the final decision principle; it allows immediate appeal from orders that are collateral to the merits of the litigation and cannot be adequately reviewed after final judgment. The exception, however, is in derogation of the federal policy against piecemeal appeals and hence is confined within strict limits. As the Supreme Court has described it,

[t]he collateral order doctrine is a "narrow exception," . . . whose reach is limited to trial court orders affecting rights that will be irretrievably lost in the absence of an immediate appeal. See Helstoski v. Meanor, 442 U.S. 500, 506-508 [99 S.Ct. 2445, 2448-49, 61 L.Ed.2d 30] (1979),. . . . To fall within the exception, an order must at a minimum satisfy three conditions: It must [1] "conclusively determine the disputed question," [2] "resolve an important issue completely separate from the merits of the action," and [3] "be effectively unreviewable on appeal from a final judgment."

Richardson-Merrell Inc. v. Koller, 472 U.S. 424, 430-31, 105 S.Ct. 2757, 2760-61, 86 L.Ed.2d 340 (1985) (quoting Coopers Lybrand v. Livesay, 437 U.S. 463, 468, 98 S.Ct. 2454, 2457, 57 L.Ed.2d 351 (1978)).

The third condition, that the order "be effectively unreviewable on appeal from a final judgment," is not satisfied by the fact that postponement of vindication may ultimately prove less efficient than an immediate review, see, e.g., Richardson-Merrell Inc. v. Koller, 472 U.S. at 436, 105 S.Ct. at 2763 ("the possibility that a ruling may be erroneous and may impose additional litigation expense is not sufficient to set aside the finality requirement imposed by Congress"); Stringfellow v. Concerned Neighbors In Action, 480 U.S. 370, 375-77, 107 S.Ct. 1177, 1181-83, 94 L.Ed.2d 389 (1987), or that ultimate vindication may require a second trial before a different trier of fact, see, e.g., Van Cauwenberghe v. Biard, 486 U.S. 517, 527-30, 108 S.Ct. 1945, 1952-54, 100 L.Ed.2d 517 (1988) (order denying motion to transfer for forum non conveniens not immediately appealable); Chasser v. Achille Lauro Lines, 844 F.2d 50, 55 (2d Cir. 1988), aff'd, 490 U.S. 495, 109 S.Ct. 1976, 104 L.Ed.2d 548 (1989) (order rejecting contractual forum-selection clause not immediately appealable); D'Ippolito v. American Oil Co., 401 F.2d 764 (2d Cir. 1968) (per curiam) (order transferring case to another district not immediately appealable).

A ruling as to whether or not there will be a jury trial does not meet the third precondition to immediate appealability under the Cohen doctrine, for such an order is entirely reviewable on appeal from the final judgment. In the present case, if the Trustee has no right to a jury trial, the Bank may raise that issue on appeal from an adverse final judgment. If the appellate court agrees with the Bank's contention, it will remand for a nonjury trial, thus vindicating the Bank's right.

CONCLUSION

We have considered all of the Bank's arguments in support of appellate jurisdiction and have found them to be without merit. We conclude that the order refusing to strike the demand for a jury trial is not reviewable under the collateral order doctrine. The appeal is dismissed for lack of appellate jurisdiction.

No costs.