dissenting.
My colleagues agree that although the district court neither dismissed the case nor ordered a stay following its order to compel arbitration, the decision is nevertheless final and thus appealable because SCI moved to dismiss instead of requesting a stay and because McCaskill agrees the court dismissed the case. They also agree, for very different reasons, to reverse the district court’s order compelling arbitration and to remand for further proceedings, presumably a trial on the merits. Because the district court did not either dismiss the case or order a stay pending arbitration, in my view its order is not a final decision and is thus not appealable. This court should remand and direct that the district court either dismiss the case or order a stay.
Longstanding federal policy strongly favors arbitration. Green Tree Fin. Corp.— Alabama, et al. v. Randolph, 531 U.S. 79, 91, 121 S.Ct. 513, 148 L.Ed.2d 373 (2000) (citing Moses H. Cone Mem’l Hasp. v. Mercury Constr. Corp., 460 U.S. 1, 24, 103 S.Ct. 927, 74 L.Ed.2d 765 (1983)). Section 16 of the Federal Arbitration Act (“FAA”) governs appellate review of arbitration orders. It provides, in relevant part, that an appeal may be taken from “a final decision with respect to an arbitration.... ” 9 U.S.C. § 16(a)(3). In addition, an appeal may not be taken from an interlocutory order “compelling arbitration....” 9 U.S.C. § 16(b)(3). The FAA does not define the term “final decision.” In Green Tree, the Supreme Court interpreted the phrase according to its well-established, plain meaning, i.e., a decision which “ends the litigation on the merits and leaves nothing more for the court to do but execute the judgment.” 531 U.S. at 86, 121 *687S.Ct. 513 (citations omitted). In addressing a district court’s order compelling arbitration and dismissing the case with prejudice, the Supreme Court held that such an order is a “final decision” and thus is immediately appealable pursuant to the FAA. Id. The Court noted, however, that if a district court enters a stay instead of a dismissal, that order is not a final, appeal-able decision under the FAA. Id. at 87, n. 2, 121 S.Ct. 513.1 See Salim Oleochemicals v. M/V Shropshire, 278 F.3d 90 (2d Cir.2002) (order compelling arbitration and dismissing without prejudice was an ap-pealable decision under the FAA); AT AC Corp. v. Arthur Treacher’s, Inc., 280 F.3d 1091 (6th Cir.2002) (order staying proceedings pending arbitration not appealable under the FAA); Interactive Flight Tech., Inc. v. Swissair Stviss Air Transp. Co., Ltd., 249 F.3d 1177 (9th Cir.2001) (order compelling arbitration and dismissing case without prejudice appealable under the FAA); Employers Ins. of Wausau v. Bright Metal Specialties, Inc., 251 F.3d 1316 (11th Cir.2001) (order compelling arbitration and dismissing the ease deemed appealable under the FAA).
Here, notwithstanding the court’s assumption to the contrary, the district court did not actually dismiss the ease. The court clearly could have ordered a stay. 9 U.S.C. § 3. Had the court issued the stay, as I see it under the appropriate procedure when compelling arbitration, any appeal at this stage would be barred. See Green Tree, 531 U.S. at 87, n. 2, 121 S.Ct. 513. There is nothing in the district court’s opinion that would allow us to infer that the court intended to dismiss the case. SCI filed a motion to compel arbitration and to dismiss the case. The district court’s order, however, merely compelled arbitration.- The order does not address, in any manner whatsoever, SCI’s request for a dismissal of the case. While it is true that SCI’s attorney stated at oral argument that the district court’s opinion effectively dismissed the case, it is well settled that parties cannot agree to jurisdiction, nor can an attorney’s assertion at oral argument establish finality in order to create appellate jurisdiction. See ITOFCA Inc. v. MegaTrans Logistics, Inc., 235 F.3d 360, 363 (7th Cir.2000). Rather, we have consistently held that “[i]t is our threshold and independent obligation to make that determination even [when] both parties agreeably [consider an] order to be final and appealable.” ITOFCA 235 F.3d at 363 (citations omitted).
Additionally, the district court’s indication that McCaskill could appeal subsequent determinations by the arbitrator is not evidence that it intended to dismiss. Rather, the statement is entirely consistent with the statutory procedure permitting judicial review of any final determination by the arbitrator. Had the court ordered a stay pending arbitration, all of the issues not resolved by this split opinion would then properly come before the district court, and perhaps before us, for full briefing and adjudication. Once a court determines that there is a valid and enforceable agreement to arbitrate and that the claims fall within the scope of the agreement, We Care Hair Dev., Inc. v. Engen, 180 F.3d 838, 844 (7th Cir.1999), it can compel arbitration. At that point the *688statute provides only that the court order a stay pending arbitration. 9 U.S.C. § 3. That should have and very well could have been what the court had in mind when it issued its order to compel arbitration. Based on the record, we do not know that the court intended to dismiss the case.
Without a dismissal of the underlying case, the district court’s order compelling arbitration remains an interlocutory order under Section 16(b)(3) of the FAA, and under Green Tree, we are not permitted to exercise jurisdiction over this case. Of course, as previously noted, the district court may also grant a stay under Section 3 of the FAA, in which case we would not have jurisdiction since it would not be ap-pealable. 9 U.S.C. § 16(b)(1); Green Tree, 531 U.S. at 87, n. 2, 121 S.Ct. 513.2 In any case, it is incumbent upon district courts to fully address and clearly dispose of a motion filed by a litigant for the parties’ benefit, to conserve its own judicial resources and to aid this court on review. See Salim Oleochemicals, 278 F.3d at 93 (urging “district courts in these circumstances to be as clear as possible about whether they truly intend to dismiss an action or mean to grant a stay ... or whether they mean to do something else entirely.”). See also Dustrol, Inc. v. Champagne-Webber, Inc., 2002 WL 122500, *4 (N.D.Tex. Jan.24, 2002) (citing Green Tree, district court clearly states that “the court dismisses this case because there are no longer any unadjudicated claims presently before the court.”).
Accordingly, I conclude that the order is not final in this case and would remand the case back to the district court for further disposition or clarification of its order.
. In resolving questions of finality, we have asked whether an appeal is from an "embedded” (those involving a request for arbitration and other relief) or “independent” (a request to order arbitration solely) proceeding. Previously, an order compelling arbitration in an independent proceeding was appealable, whereas one in an embedded proceeding was interlocutory. See Napleton v. General Motors Corp., 138 F.3d 1209, 1212 (7th Cir.1998). The Supreme Court, however, rejected this distinction in Green Tree, 531 U.S. at 88, 121 S.Ct. 513.
. I pause to take note of an issue left unresolved by the Supreme Court in Green Tree, i.e., whether a district court may dismiss a case under the FAA at all. Green Tree, 531 U.S. at 87 n. 2, 121 S.Ct. 513 (declining to address whether district court should have entered a stay, rather than a dismissal). The plain language of the FAA gives a court only the power to grant a stay. See 9 U.S.C. § 3. In contrast, nothing in the FAA refers to the district court's power to dismiss a case. See also Stephen H. McClain, Under a New Supreme Court Decision, Litigants Seeking Arbitration of a Dispute can Control the Timing of an Appeal, 48-Aug. Fed.Law. 22, 25 (2001) (noting that, during oral argument of Green Tree, some of the justices questioned whether or not a stay was required under the FAA). This court has also questioned whether there is any statutory authority for dismissing a case when compelling arbitration. See Kroll v. Doctor’s Assoc., Inc., 3 F.3d 1167, 1172 (7th Cir.1993). The uncertainty surrounding a district court’s ability, or authority, to dismiss a case under the FAA is yet another reason to decline jurisdiction over this appeal.