OPINION

PowerAgent Inc. (“PowerAgent”) appeals the district court’s orders striking its Amended Complaint and confirming an arbitration award in favor of Electronic Data Systems Corp. (“EDS”). Because Power-Agent itself argued that the arbitration panel should independently determine the arbitrability of all its claims and fails to provide a sufficient basis to vacate the arbitration award, we affirm.

I

PowerAgent’s initial complaint in district court alleged that EDS breached several interrelated contracts — a Services Agreement and two investment agreements— and committed RICO violations. The Services Agreement between PowerAgent and EDS contained the following arbitration clause:

Pursuant to that agreement, EDS filed a motion to dismiss or stay the complaint and compel arbitration. The district court found that, consistent with the initial complaint, the contracts were interrelated, and that the claims in the complaint were subject to the arbitration agreement.

After the district court found that the claims in PowerAgent’s first complaint were subject to arbitration, PowerAgent amended its complaint to: (1) focus on an additional, later, oral agreement, concerning further investments, that contained no arbitration clause; (2) drop its RICO claim; and (3) omit any reference to the interrelationship it had previously asserted between the service agreements and the investment agreements. The district court granted EDS’s motion to strike the Amended Complaint on the ground that, among other reasons, a plaintiff should not be allowed to contradict allegations in a prior complaint to avoid arbitration.

Following the determination of arbitra-bility and the decision to strike the Amended- Complaint, PowerAgent petitioned this court for -a writ of mandamus directing the district court to (1) vacate its order striking the Amended Complaint; (2) determine whether the claims in the Amended Complaint are arbitrable; and (3) retain jurisdiction over the non-arbitra-ble claims. See PowerAgent, Inc. v. United States Dist. Court for the N. Dist. of Cal., 210 F.3d 385 , 2000 WL 32073 , at *1 (9th Cir. Jan.14, 2000). This court denied the petition, stating:

Id. at *2 (citations omitted).

After this court denied the petition, PowerAgent filed a Notice of Arbitration with the American Arbitration Association regarding the claims in the Complaint and the Amended Complaint. PowerAgent asserted that the arbitration panel, not the district court, should determine arbitrability arid asked the arbitrators independently to address whether all them claims were arbitrable. Specifically, PowerAgent argued:

After briefing and oral argument, the arbitrators unanimously determined that all the claims in the dispute, including the claims added in the Amended Complaint, were subject to the arbitration clause. In the Order Regarding Jurisdiction, the arbitrators stated:

Following extensive proceedings, the arbitration panel found in favor of EDS on the merits of all the disputes.

PowerAgent moved to vacate the arbitration award and EDS cross-moved to confirm the award. The district court confirmed the award, finding that “[a]ll decisions made by the Arbitrators, including their findings on arbitrability, waiver, and the merits, were within their authority and in no instance constituted a manifest disregard of the law.”

II

The law of the case does not preclude PowerAgent from challenging the statement in this court’s mandamus decision that a plaintiff may not drop factual allegations in an effort to avoid arbitration. A denial of a petition for mandamus usual ly does not constitute the law of the case, because of the special limitations on granting such a writ. Kirshner v. Uniden Corp. of Am., 842 F.2d 1074, 1078-79 (9th Cir.1988) (citations omitted). Only when the decision to deny the writ was on the merits does the law of the case doctrine apply to mandamus actions. See id. Where the denial is or may be the result of the special limitations applying to the writ, the second panel is not bound by the earlier decision and thus need not speculate as to whether the decision was on the merits. See id.

In this case, the previous panel did address the merits of PowerAgent’s argument, but only in the context of the special limitations on granting an extraordinary writ. See PowerAgent, 210 F.3d 385 , 2000 WL 32073 at *1 (noting that mandamus is a drastic and extraordinary remedy and concluding that PowerAgent failed to meet the particular factors including clear error). Such emphasis on the special limitations of mandamus precludes applying the law of the case doctrine in this instance. See Kirshner, 842 F.2d at 1078-79 . Thus, this panel is not bound by the reasoning of the previous panel as we review the district court’s order confirming the arbitration award.

Ill

We nonetheless conclude, without reaching the question whether the district court should have allowed the filing of the Amended Complaint in the first instance, that PowerAgent is now bound by the arbitrators’ decision that this entire dispute — encompassing both the original and the Amended Complaint — was arbitrable.

Arbitrability is ordinarily for courts, not arbitrators, to decide unless the parties agree otherwise. “Courts should not assume that the parties agreed to arbitrate arbitrability unless there is ‘clea[r] and unmistakeabl[e]’ evidence that they did so.” First Options v. Kaplan, 514 U.S. 938, 944 , 115 S.Ct. 1920 , 131 L.Ed.2d 985 (1995) (citing AT & T Techs. v. Communications Workers, 475 U.S. 643, 649 , 106 S.Ct. 1415 , 89 L.Ed.2d 648 (1986)). Where parties do agree to arbitrate the issue of arbitrability, courts give the arbitrators’ conclusion regarding arbitrability the same respect otherwise accorded arbitrators’ decisions. Id. at 943, 115 S.Ct. 1920 .

Here, as will appear, neither paradigm quite fits. Whether or not the parties agreed with one another to arbitrate the arbitrability issue, PowerAgent affirmatively submitted the issue to the arbitrators and urged that they had power to decide it. The question we face is whether PowerAgent, dissatisfied with the answer to the question it insisted the arbitrators could and should decide, can now ask us to determine that the arbitrators in fact lacked authority to determine the arbitra-bility question.

Contrary to PowerAgent’s submission, First Options does not resolve the question before us. In First Options , the defendants in arbitration filed with the arbitrators a memorandum opposing the arbitrators’ jurisdiction. Id. at 946 , 115 S.Ct. 1920 . The Supreme Court concluded that that submission did not signify an agreement to submit the question of arbitrability to the arbitrator:

Id. (emphasis in original). The Court therefore held that the arbitrator’s decision of arbitrability was to be reviewed de novo. Id. at 944 , 115 S.Ct. 1920 .

PowerAgent’s position in this case is quite different from that of the defendants’ posture in First, Options. PowerAgent was the plaintiff in arbitration and affirmatively sought to submit the issue of arbitrability to the arbitration panel, arguing in favor of the arbitrators’ authority to decide the issue.

PowerAgent outlined its position in its Amended Notice of Arbitration:

Although EDS argued that the arbitration panel was bound by the district court’s order, PowerAgent clearly requested that the arbitration panel independently address the issue of arbitrability and maintained that it had the authority to do so:

Having affirmatively urged the arbitrators to decide arbitrability and asserted their authority to do so, PowerAgent cannot await the outcome and, after an unfavorable decision, challenge the authority of the arbitrators to act on that very issue. We so held in closely analogous circumstances in’ Tristar Pictures, Inc. v. Dir.’s Guild of Am., 160 F.3d 537, 540 (9th Cir.1998) (citing Ralph Andrews Prods., Inc. v. Writers Guild of Am., West, 938 F.2d 128, 130 (9th Cir.1991)). Unlike in First Options , in Tristar Pictures, the court found that the party seeking a judicial determination regarding arbitrability had clearly evinced its intent to be bound by the arbitrators’ decision on the question. Tristar Pictures, 160 F.3d at 540 . We held that where there is clear evidence of a party’s intent to be bound by the arbitrator’s decision on the issue of arbitrability, that party is estopped from later changing its position and challenging the arbitrator’s authority to determine the issue of arbitra-bility. Id.

Although Tristar did not so indicate, its holding is closely analogous to the doctrine of judicial estoppel — that is, the principle that a litigant may not benefit by making directly contradictory arguments regarding the same dispute in different tribunals. See Hamilton v. State Farm, Fire & Cas. Co., 270 F.3d 778, 782-83 (9th Cir.2001) (holding that judicial estoppel precludes a party from gaining an advantage by asserting one position and then later — after a tribunal relied on or accepted that position — taking a clearing incon sistent position in either the same litigation or a different case concerning the same dispute).

Tristar Pictures involved a collective bargaining agreement (“CBA”), while this case does not, and in this circuit CBAs have been held to be outside the coverage of the Federal Arbitration Act (“FAA”). Kemner v. Dist. Council of Painting and Allied Trades No. 86, 768 F.2d 1115 , 1118 n. 1 (9th Cir.1985). The FAA did apply in First Options and does apply here. No reason appears, however, why the same estoppel principle at work in Tristar Pictures should not apply to this case, as it is fully consistent with concerns discussed in First Options .

PowerAgent was not required to present the issue of arbitrability of the Amended Complaint to the arbitrators. Indeed, EDS argued that the district court had already determined that the dispute was arbitrable and that the arbitrators did not have authority to decide otherwise. After the petition for mandamus was denied, PowerAgent could have arbitrated only the original complaint, awaited a final resolution of the case, and then appealed the decision of the District Court to strike the Amended Complaint. Instead, PowerA-gent voluntarily requested that the arbitration panel address the arbitrability of the entire dispute including the Amended Complaint and affirmatively argued that the arbitrators had the authority to do so. Once it determined that the claims in the Amended Complaint were arbitrable, the arbitration panel resolved those claims in EDS’s favor. PowerAgent is now bound by the arbitration panel’s findings on arbi-trability and the merits unless it can overcome the highly deferential standard of review employed by the federal courts regarding arbitrators’ holdings. See, e.g., San Martine Compania De Navegacion v. Saguenay Terminals Ltd., 293 F.2d 796, 801 (9th Cir.1961).

The district court, therefore, correctly applied a deferential standard of review to the arbitrators’ decisions. See id. (holding that an arbitration award will not be vacated unless it exhibits a “manifest disregard of the law”). While we review de novo the decision to vacate or confirm an arbitration award, review of the award itself is “both limited and highly deferential” and an arbitration award may be vacated only if it is “completely irrational” or “constitutes manifest disregard of the law.” Coutee v. Barington Capital Group, 336 F.3d 1128 , 1132-33 (9th Cir.2003).

There is nothing in the arbitration panel’s decisions to suggest that they are either completely irrational or constitute a manifest disregard of the law. On the contrary, the arbitrators addressed the issues presented to them by the parties and reached findings based on the evidence provided. With regard to the arbitrability of the Amended Complaint, the issue now in dispute, the arbitration panel held that the claims in the Amended Complaint were subject to the arbitration clause in the Services Agreement because the written contracts and the purported subsequent oral contracts were interrelated, as part of the same ongoing transaction or series of transactions.

In particular, the arbitration panel found that the investment commitments were made in exchange for PowerAgent’s commitments to engage EDS’s services, and that the money invested was intended in part to pay for those services. As to the last oral commitment for further investments, again the intended quid pro quo was a change in the Services Agreement favorable to EDS. Nothing about this analysis is completely irrational or manifestly disregards the law. We therefore affirm the district court’s order confirming the arbitration award.

AFFIRMED.

. The Supreme Court overruled our prior precedent that the FAA does not apply to any employment contracts and held, in a case involving an individual employment contract, that the FAA applies to all individual employment contracts except those involving transportation workers. Circuit City Stores, Inc. v. Adams, 532 U.S. 105, 109 , 121 S.Ct. 1302 , 149 L.Ed.2d 234 (2001). Circuit City did not address a CBA, and we have not considered, and do not here consider, its application to such agreements. See Textile Workers Union v. Lincoln Mills, 353 U.S. 448, 451-52 , 77 S.Ct. 912 , 1 L.Ed.2d 972 (1957) (holding that collective bargaining agreements are enforceable under § 301 of the Labor Management Relations Act, 29 U.S.C. § 185 , over Justice Frankfurter's dissent noting implicit rejection by the majority of FAA coverage).