POSNER, Circuit Judge.

Before us is an interlocutory appeal in a diversity case governed by Illinois law. Hennessy Industries, a large manufacturer of car parts that has been beset by asbestos-related personal injury claims, has been seeking coverage by National Union Fire Insurance Company of Pittsburgh, PA, of asbestos claims against Hennessy that date from the 1980s. The companies entered into a confidential Cost Sharing Agreement in 2008, and as claims against Hennessy by asbestos victims came rolling in, Hennessy asked National Union to indemnify it for settlement and defense costs, as provided in the agreement. But the two parties couldn't agree over what was owed. According to Hennessy, National Union withheld payments due Hennessy under the agreement and violated it in other ways. To resolve their differences Hennessy demanded arbitration in accordance with a provision of the agreement that provides for arbitration of disputes between the parties and instructs the arbitrators to apply Illinois law.

Last year Hennessy filed the suit out of which this appeal arises. It is a suit under 215 ILCS 5/155(1), a section of the Illinois Insurance Code captioned "Attorney fees," which provides that

Hennessy claimed that National Union's delays in providing coverage of the asbestos claims had been vexatious and unreasonable. National Union, contending that the arbitration clause in the cost-sharing agreement required arbitration of Hennessy's section 155 claim ("section 155" is the parties' shorthand for section 5/155(1)) as well as of the parties' other disputes, moved the district court to order arbitration and dismiss Hennessy's suit. The district judge denied the motion on the basis both of a statement in the arbitration clause that "the arbitrators shall not be empowered or have jurisdiction to award punitive damages, fines or penalties," and the judge's belief that Hennessy's claim arose under Illinois statutory law rather than under the cost-sharing agreement. National Union appeals the denial pursuant to 9 U.S.C. §§ 16(a)(1)(A), (B), which are provisions of the Federal Arbitration Act that authorize appeal from orders denying referral to arbitration in a class of cases that includes Hennessy's litigation with National Union.

Had National Union been asking the district court to intervene in the arbitrators' adjudication, the court would not have had jurisdiction. A party to arbitration can't, while the arbitration of an issue is proceeding, ask a court, whether the district court or this court, to weigh in on the issue. "A party's request to tell an arbitrator how to act in a pending proceeding is not a request to compel arbitration, no matter what caption the litigant puts on its motion.... Judges must not intervene in pending arbitration to direct arbitrators to resolve an issue one way rather than another. Review comes at the beginning or the end, but not in the middle. Once the arbitration is over, the losing side can seek judicial review." Central States, Southeast & Southwest Areas Pension Fund v. U.S. Foods, Inc., 761 F.3d 687, 689 (7th Cir.2014) (citations and interior quotation marks omitted); see also Blue Cross Blue Shield of Massachusetts, Inc. v. BCS Ins. Co., 671 F.3d 635, 637-38 (7th Cir.2011). But that is not this case. National Union is asking that an additional issue be submitted to arbitration, rather than that the arbitrator be instructed to resolve an issue in an existing arbitration a certain way. The district judge's denial of the request is therefore within the scope of 9 U.S.C. § 16(a)(1)(B), which authorizes an interlocutory appeal from an order "denying a petition ... to order arbitration to proceed." So the district court had, and we have, jurisdiction.

National Union makes several arguments for reversal of the denial of its motion to compel arbitration and dismiss Hennessy's suit. One is that the passage the district judge quoted from the arbitration clause in the cost-sharing agreement — "the arbitrators shall not be empowered or have jurisdiction to award punitive damages, fines or penalties" — is a waiver of any claim that Hennessy might have under section 155; the fact that the cost-sharing agreement tells the arbitrator to apply substantive Illinois law just means that Illinois law rather than some other body of law is to govern; it does not preclude waivers. But National Union's main argument is that the cost-sharing agreement requires arbitration of "any dispute" that requires "interpretation" of the agreement, and because the finder of fact will have to interpret that agreement in order to determine whether it was violated "vexatiously" or "unreasonably" Hennessy's section 155 claim requires an interpretation of the cost-sharing agreement and must therefore be arbitrated.

Those are persuasive arguments; National Union's further argument that the Federal Arbitration Act preempts section 155 of the Illinois Insurance Code is not. The McCarran-Ferguson Act, 15 U.S.C. § 1011 et seq., provides that no federal statute "shall be construed to invalidate, impair or supersede any law enacted by any State for the purpose of regulating the business of insurance." § 1012(b). And section 155 is a state regulation of the insurance business. Apart from the fact (not itself decisive) that it is part of the state's insurance code, it is concerned only with the conduct of insurance companies, specifically delay by them in paying claims to their insureds. The case is thus unlike Pilot Life Ins. Co. v. Dedeaux, 481 U.S. 41, 107 S.Ct. 1549, 95 L.Ed.2d 39 (1987), which held that ERISA preempted an ERISA beneficiary's state common law cause of action, and noted that the state law under which that cause of action arose was not a regulation of the insurance business within the meaning of the McCarran-Ferguson Act.

Hennessy cites a line of Illinois intermediate appellate court decisions, culminating in Amerisure Mutual Ins. Co. v. Global Reinsurance Corp. of America, 399 Ill.App.3d 610, 340 Ill.Dec. 1, 927 N.E.2d 740, 751-52 (2010), that hold that arbitrators have no authority to enforce section 155 because it provides that if specified conditions are met "the court may allow as part of the taxable costs in the action reasonable attorney fees, other costs, plus an amount not to exceed [etc.]" (emphasis added). It's odd that Hennessy should take that position, since it disables it from seeking penalties in arbitration (thus compelling it to sue in court) — and it is penalties that it's seeking under section 155. The holding by the intermediate appellate court (the state's supreme court has not opined on the issue) in the Amerisure case is, moreover, highly vulnerable, because it is wooden. Section 155 is about remedies rather than about jurisdiction or venue. When antagonists agree to arbitrate a dispute that could be made the subject of a court suit, an arbitrator or panel of arbitrators is substituted for a court. Antitrust claims arising under the Sherman Act, for example, are arbitrable, although they are within the exclusive jurisdiction of the federal courts. Mitsubishi Motors Corp. v. Soler Chrysler-Plymouth, Inc., 473 U.S. 614, 105 S.Ct. 3346, 87 L.Ed.2d 444 (1985). What is excluded is not arbitration but suing in state court.

We can't think why arbitrators would be thought incompetent to enforce section 155, especially since if the parties don't want it enforced they can, as in this case, agree in the arbitration clause to deny the arbitrators the authority to enforce it. Hennessy is not some hapless consumer who has to be protected by the courts from improvidently consenting to arbitrate a dispute with a big bad seller.

National Union is correct, moreover, that Hennessy in the agreement indeed waived any right to ask the arbitrator to award punitive damages, fines, or penalties for National Union's allegedly unreasonable delay in honoring Hennessy's claims. Having submitted a dispute to arbitration that explicitly excludes a particular remedy, a party can't sue in court for the excluded remedy.

And recurring to our earlier point that section 155 is procedural rather than substantive, we note that it provides a remedy in a specified type of "action" (case); it does not create a cause of action; it presupposes rather than authorizes a suit. If the court in which the specified type of action is brought finds that a party is causing a delay that is "vexatious and unreasonable," then it can levy a penalty specified in section 155-in the same action. Section 155 "simply provides an extracontractual remedy to an action on a policy." Cramer v. Insurance Exchange Agency, 174 Ill.2d 513, 221 Ill.Dec. 473, 675 N.E.2d 897, 902 (1996). This interpretation makes good sense. Allowing two bodies to adjudicate the same case wastes resources and risks contradictory outcomes.

It's true that Smith v. State Farm Insurance Companies, 369 Ill.App.3d 478, 308 Ill.Dec. 118, 861 N.E.2d 183 (2006), allowed a suit based solely on section 155. But the only issue discussed by the court was whether the suit was barred by an arbitration agreement. And Smith was an intermediate appellate decision, rather than a decision by the state's highest court. Cramer, cited above, a state supreme court decision that we followed in Westchester Fire Insurance Co. v. General Star Indemnity Co., 183 F.3d 578, 586 (7th Cir.1999), teaches that section 155 creates a remedy, not a cause of action.

In summary, the district court's order is reversed and the court is instructed to order arbitration of Hennessy's section 155 claim and dismiss its suit.