
347 S.W.3d 897 (2011)
AUSTIN COMMERCIAL CONTRACTORS, L.P., Appellant,
v.
CARTER & BURGESS, INC., Appellee and
In re Austin Commercial Contractors, LP, Relator.
No. 05-10-01542-CV.
Court of Appeals of Texas, Dallas.
August 15, 2011.
Rehearing Overruled September 29, 2011.
*898 Gregory Harwell, Stacy R. Obenhaus, Matthew M. Waterman, Gardere Wynne Sewell LLP, for Appellant.
Andrew Derald Keetch, Stephen L. Tatum, Ryan Logan Valdez, John S. Polzer, Cantey & Hanger, L.L.P., for Appellee.
Before Justices MORRIS, FITZGERALD, and FRANCIS.

OPINION
Opinion By Justice FITZGERALD.
In this consolidated interlocutory appeal and mandamus proceeding, Austin Commercial Contractors, L.P. ("ACCLP") challenges the trial court's October 29, 2010 Order Regarding Plaintiff's Motion to Compel Arbitration, which both compels arbitration and orders the arbitration to proceed before the American Arbitration Association (the "AAA"). We dismiss the interlocutory appeal for lack of jurisdiction, but we conditionally grant the petition for mandamus.

Background
The Regents of the University of California entered into an agreement with ACCLP (the "Prime Contract") for the latter to act as general contractor on a project involving construction of a new building at the Los Alamos National Laboratories in New Mexico.[1] As general contractor, *899 ACCLP entered into a Consultant Agreement with Carter & Burgess to provide all architectural and engineering services required by the project. ACCLP sued Carter & Burgess alleging breach of contract. Carter & Burgess answered subject to a motion to dismiss. It also served discovery and asserted a counterclaim for breach of contract.
Approximately two and one half months after filing suit, ACCLP filed a motion to compel arbitration pursuant to the Consultant Agreement. It relied on a clause in that agreement which states:
19.1 Any controversy or claim arising out of or relating to this Agreement or the breach thereof shall be subject to the dispute resolution procedures, if any, set out in the Prime Contract between [ACCLP] and [LANS]. Should the Prime Contract contain no specific requirement for the resolution of disputes, any such controversy or claim shall be resolved by arbitration pursuant to the Construction Industry Rules of the American Arbitration Association then prevailing, and judgment upon the award by the Arbitrator(s) shall be entered in any Court having jurisdiction thereof.
The Prime Contract does contain specific requirements for dispute resolution: submission of the dispute to mediation and thenif not resolvedto binding arbitration before the Civilian Board of Contract Appeals (the "CBCA").[2] ACCLP's motion sought two specific rulings: the parties should be compelled to arbitration, and the arbitration should proceed before the CBCA.
Carter & Burgess opposed the motion. It contended that the CBCA lacked jurisdiction over a dispute between ACCLP and Carter & Burgess, that there was no agreement requiring it to arbitrate before the CBCA, and that the CBCA could not assume jurisdiction merely through agreement of the parties. Carter & Burgess also contended that ACCLP had waived its right to elect arbitration by filing suit. And, alternatively, Carter & Burgess argued that if the agreements do require arbitration before the CBCA, then ACCLP had failed to satisfy conditions precedent to arbitration.
The trial court's October 29, 2010 order granted the motion in part and denied it in part.[3] It ordered the matter to proceed to arbitration as ACCLP had requested; neither party challenges that ruling in this Court. But the order also ordered the arbitration to proceed before the AAA. ACCLP appealed and sought mandamus relief as to this ruling. We consolidated the two proceedings for resolution in this Court.

Interlocutory Appeal
In 2009, the Texas Legislature added a provision to the civil practice and remedies code addressing interlocutory appeals *900 arising under the Federal Arbitration Act:
In a matter subject to the Federal Arbitration Act (9 U.S.C. Section 1 et seq.), a person may take an appeal or writ of error to the court of appeals from the judgment or interlocutory order of a district court, county court at law, or county court under the same circumstances that an appeal from a federal district court's order or decision would be permitted by 9 U.S.C. Section 16.
TEX. CIV. PRAC. & REM.CODE ANN. § 51.016 (West Supp.2011). The parties agree any arbitration ordered will be governed by the Federal Arbitration Act. Thus, an interlocutory appeal in this case will be permitted only if it would be permitted under the same circumstances under section 16. See CMH Homes v. Perez, 340 S.W.3d 444, 449 (Tex.2011). Section 16, in turn, allows appeals from:
(1) an order
(A) refusing a stay of any action under section 3 of this title,
(B) denying a petition under section 4 of this title to order arbitration to proceed,
(C) denying an application under section 206 of this title to compel arbitration,
(D) confirming or denying confirmation of an award or partial award, or
(E) modifying, correcting, or vacating an award;
(2) an interlocutory order granting, continuing, or modifying an injunction against an arbitration that is subject to this title; or
(3) a final decision with respect to an arbitration that is subject to this title.
9 U.S.C. § 16(a) (West 2009). Section 16 goes on to identify interlocutory orders that will not support an immediate appeal:
(1) granting a stay of any action under section 3 of this title;
(2) directing arbitration to proceed under section 4 of this title;
(3) compelling arbitration under section 206 of this title; or
(4) refusing to enjoin an arbitration that is subject to this title.
Id. § 16(b).
It is clear the portion of the trial court's order compelling arbitration would not be appealable under federal law, so it is not appealable in this case. See id § 16(b)(3). The portion of the court's order directing arbitration to proceed before the AAA actually speaks to the rules under which the arbitration shall take place. (The Prime Contract directs the Board to arbitrate all claims "in accordance with the Rules of the Board; the Consultant Agreement directs resolution, when appropriate, "by arbitration pursuant to the Construction Industry Rules of the [AAA].") We find no provision in section 16 permitting appeal of such an order. Accordingly, we conclude this portion of the trial court's order is not appealable either. See CMH Homes, 340 S.W.3d at 451. Our conclusion comports with the rule that section 16 "generally permits immediate appeal of orders hostile to arbitration, whether the orders are final or interlocutory, but bars appeal of interlocutory orders favorable to arbitration." See Green Tree Fin. Corp.-Alabama v. Randolph, 531 U.S. 79, 86, 121 S.Ct. 513, 148 L.Ed.2d 373 (2000); In re Gulf Exploration, LLC, 289 S.W.3d 836, 839 (Tex.2009).
The trial court's order is not appealable under section 16. Accordingly we dismiss ACCLP's interlocutory appeal for lack of jurisdiction. See TEX. CIV. PRAC. & REM. CODE ANN. § 51.016.[4]


*901 Petition for Mandamus
To show itself entitled to mandamus, a relator must show that (1) the trial court clearly abused its discretion, and (2) the relator has no adequate remedy by appeal. Gulf Exploration, 289 S.W.3d at 842. Mandamus is generally unavailable if the order at issue compels arbitration: even if the relator can meet the first prong of this test by showing an abuse of discretion, it can rarely meet the second prong. Id. Indeed, "[i]f a trial court compels arbitration when the parties have not agreed to it, that error can unquestionably be reviewed by [final] appeal." Id. Although parties may expend time and money if they are ordered to arbitration improperly, delay and expensestanding alonewill not render the final appeal inadequate. Id. That rule is especially true when the substance of the arbitration is a contract claim, because the party that prevails can recover its fees and expenses. Id. The case before us involves only contract claims, and it does not implicate any conflicting legislative mandates. See id. (identifying rare exception when mandamus may allow appellate court to give direction to law that would otherwise prove elusive in appeal from final judgment). Thus, the parties have an adequate remedy by appeal with which to make their challenges, if any, to the portion of the trial court's order compelling arbitration.
ACCLP contends, however, that it has no adequate remedy by appeal for the second portion of the trial court's order, which requires the arbitration to proceed under AAA rules rather than the rules of CBCA. We must agree. Parties may specify by contract the rules under which their arbitration will be conducted, and enforcing those rules according to the terms of the agreement is fully consistent with the goals of the FAA. Volt Info. Sci., Inc. v. Bd. of Trustees of Leland Stanford Junior Univ., 489 U.S. 468, 479, 109 S.Ct. 1248, 103 L.Ed.2d 488 (1989). And there is no adequate remedy by appeal when a party is erroneously denied its contracted-for arbitration rights under the FAA. In re D. Wilson Const. Co., 196 S.W.3d 774, 780-81 (Tex.2006).
Recently, in CMH Homes v. Perez, 340 S.W.3d 444 (Tex.2011), our supreme court addressed a case in which the parties had contracted to name their arbitrator but were unable to reach agreement on the issue. The trial court intervened and appointed an arbitrator. CMH Homes filed an interlocutory appeal challenging the appointment and requesting, in the alternative, that its appeal be treated as a petition for mandamus. Id. at 446. The court of appeals concluded it lacked jurisdiction to hear the interlocutory appeal, and the supreme court affirmed that ruling. Id. at 452. However, the supreme court concluded the court of appeals erroneously declined to treat the appeal as a mandamus proceeding. Id. at 454. In reaching that conclusion, the supreme court cited In re Louisiana Pacific Corp., 972 S.W.2d 63 (Tex.1998), in which the court had concluded a trial court's order appointing an arbitrator could be reviewed by mandamus. 340 S.W.3d at 452. The court stated that its holding in Louisiana Pacific was not altered by the Legislature's adoption of section 51.016 because "[t]here is still no remedy by appeal because the FAA does not provide for the review of this type of order in state court." Id. The court stressed there is no adequate remedy by appeal when a party is denied its contractual arbitration rights. Id. (citing D. Wilson, 196 S.W.3d at 780). We conclude we are bound by this principle in the case before us: if the trial court denied AACLP *902 its contractual arbitration rights by ordering arbitration before the AAA, then ACCLP will lack an adequate remedy by appeal.
We further conclude the trial court clearly abused its discretion in compelling arbitration to proceed under the rules of the AAA. The Consultant Agreement unambiguously provides that any claim arising out of or relating to the breach of that agreement "shall be subject to the dispute resolution procedures, if any, set out in the Prime Contract." And, as we discussed above, the Prime Contract does set out specific dispute resolution procedures, which are centered on binding arbitration under the rules of the CBCA. Thus, the back-up procedure of arbitration before the AAA should not have been implicated unless Carter & Burgess identified a reason the Prime Contract's dispute resolution procedure was, in essence, non-existent. But Carter & Burgess's objections to the jurisdiction of the CBCA and its contention that ACCLP has failed to satisfy conditions precedent to arbitration are matters of procedure that are for the arbitrator and not for the court. See Howsam v. Dean Witter Reynolds, Inc., 537 U.S. 79, 84-85, 123 S.Ct. 588, 154 L.Ed.2d 491 (2002) (questions of procedural arbitrability are matters for arbitrator to decide); see also Am. Realty Trust, Inc. v. JDN Real EstateMcKinney, L.P., 74 S.W.3d 527, 531 (Tex.App.-Dallas 2002, pet. denied) (question whether any contractually-based prerequisites to arbitration have been satisfied is for arbitrator). Nor are we persuaded by Carter & Burgess's argument that by initiating arbitration before the AAAas it was ordered to do ACCLP has waived its right to complain of arbitration in that forum.

Conclusion
We dismiss ACCLP's interlocutory appeal for lack of jurisdiction. We conditionally grant the petition for mandamus insofar as it complains of the portion of the October 29, 2010 order that orders the arbitration to proceed before the AAA. We direct the trial court (1) to vacate that portion of its order, and (2) to amend the order to require the arbitration to proceed as directed by the Prime Contract, under the rules of the CBCA. We are confident the district court will comply without delay. The writ will issue only if it does not.
NOTES
[1]  The contract identified the building as the CMRR Radiological Laboratory/Utility/Office Building. The University was later replaced under the Prime Contract by Los Alamos National Security, LLC ("LANS").
[2]  The former DOE Board of Contract Appeals (the "Board") is the entity actually identified as the proper forum for arbitration under the Prime Contract. However, the CBCA has authority to hear claims for the Board, which no longer exists. See 41 U.S.C.A. § 438(c)(2)(A) (West 2008) (CBCA may assume jurisdiction over disputes over which board of contract appeals exercised jurisdiction before effective date of statute, i.e., Jan. 6, 2007).
[3]  We reject either party's argument that this proceeding involves any order other than the October 29, 2010 Order Regarding Plaintiff's Motion to Compel Arbitration. The order refers to hearings held on three earlier dates, but neither letters nor oral pronouncements following those hearings contain the trial court's final rulings on the arbitration issues.
[4]  Carter & Burgess's Motion to Dismiss Appeal was referred to this panel for resolution. The motion urged dismissal based on estoppel, because ACCLP had purportedly accepted the benefits of arbitration before AAA by initiating a proceeding there after the trial court signed the order at issue in this proceeding. Our opinion today, dismissing the appeal on jurisdictional grounds, renders the motion moot. It is denied on that basis.
