This appeal presents a pair of issues arising out of a fee dispute between a law firm, Meierhenry Sargent LLP, and two dissatisfied clients, Bradley and Kerry Williams. After removing the firm's lawsuit seeking to recover its unpaid fees to federal court, the Williamses stayed the action to allow the unpaid-fees claim to proceed in arbitration.

Once in arbitration, the Williamses raised numerous counterclaims and defenses. The firm asked the district court for "relief from [the] stay" and a "declar[ation] [addressing] the scope of the arbitration proceedings." In effect, what the firm sought was a ruling that the Williamses had to pursue most of their counterclaims in court, not in arbitration.

The district court largely agreed with the firm's request and issued an order dividing the counterclaims into two categories: those the Williamses could raise in arbitration and those they could not. The Williamses ask us to reverse the part of the order denying them the ability to arbitrate some of their counterclaims. We vacate one threshold finding that should have been left for the arbitrators to decide but otherwise affirm.

I.

The first question is whether we can hear this appeal at all. The district court has not yet entered a final judgment, see 28 U.S.C. § 1291 , so the Williamses urge us to conclude that this is an appeal from "an interlocutory order granting ... an injunction against an arbitration," which we have jurisdiction to review under 9 U.S.C. § 16 (a)(2). The trouble is that the district court did not say it was granting an injunction, nor does its order purport to enjoin the Williamses from arbitrating their claims. Rather, the order simply declares that certain counterclaims "are not before the [a]rbitration panel," while others "remain in arbitration."

Our jurisdiction rests on the substance of the order, however, not simply what the district court chose to call it. In Conners v. Gusano's Chicago Style Pizzeria , for example, we accepted an interlocutory appeal from an order that "prevent[ed] [a party] from using its agreement with [other parties] to relocate a dispute to an arbitral forum." 779 F.3d 835 , 839 (8th Cir. 2015). We looked past the "label" affixed to the order and emphasized its "injunctive effect," which was to deny an "arbitral forum" with "finality." Id. (quoting Nordin v. Nutri/Sys., Inc. , 897 F.2d 339 , 342 (8th Cir. 1990) ); see also Gulfstream Aerospace Corp. v. Mayacamas Corp. , 485 U.S. 271 , 287-88, 108 S.Ct. 1133 , 99 L.Ed.2d 296 (1988) (explaining that appellate jurisdiction extends to "orders that have the practical effect of granting or denying injunctions and have serious, perhaps irreparable, consequence" (internal quotation marks and citation omitted) ).

To be sure, Conners relied on a general statutory grant of jurisdiction over interlocutory orders "granting ... injunctions," rather than the arbitration-specific provision we rely on here. 779 F.3d at 839 (citing 28 U.S.C. § 1292 (a)(1) ); cf.

McLaughlin Gormley King Co. v. Terminix Int'l Co. , 105 F.3d 1192 , 1193 (8th Cir. 1997) (explaining that "appealability [in the arbitration context] is governed by the specific appeal provisions" in 9 U.S.C. § 16 ). But other than the fact that the arbitration-specific provision is narrower, the operational language in both statutes is the same: they allow appeals from interlocutory orders "granting" an injunction. So labels are no more decisive under one than the other.

We add that we are unsure what else the district court's order could be, if not an injunction against arbitration. The firm asked the court to declare the scope of the arbitration, but federal courts do not have that sort of general supervisory authority over ongoing arbitration proceedings. Cf. 9 U.S.C. § 16 (listing various orders a district court might issue in connection with an arbitration). To the contrary, the most natural way the district court could have granted the relief the firm sought was by enjoining the Williamses from arbitrating some of their counterclaims. Accordingly, we have appellate jurisdiction under 9 U.S.C. § 16 (a)(2).

II.

We now turn to the question of whether the counterclaims enjoined by the district court were arbitrable. When arbitrability depends on the interpretation of a contract, as it does here, our review is de novo. See Lyster v. Ryan's Family Steak Houses, Inc. , 239 F.3d 943 , 945 (8th Cir. 2001). We review any underlying factual findings, however, for clear error. See id.

The fee dispute arose out of work the firm did in connection with a proposed oil pipeline across the Williamses' property in South Dakota. In their view, the firm neglected and mishandled their case from the beginning and ignored their instructions regarding negotiations to settle a condemnation action brought by the company seeking to build the pipeline. They officially ended the representation once they learned that a trial had been scheduled for dates the firm was reportedly unavailable, which they took to mean that the firm had effectively withdrawn and was leaving them "on their own to deal with the trial themselves."

In response to the firm's efforts to get paid for its work, the Williamses attempted to raise the following counterclaims in the arbitration, all under South Dakota law: breach of contract, anticipatory breach of contract, estoppel, forfeiture, negligence, breach of fiduciary duty, deceit, and defamation. They also sought a declaration that they did not owe money to the firm.

The district court ruled that the Williamses could not arbitrate part of their breach-of-contract claim; their negligence and breach-of-fiduciary-duty claims to the extent they sought to recover damages; and their anticipatory-breach, deceit, and defamation claims. The Williamses argue that the court should have allowed each of these claims to proceed in arbitration. 1

The question is whether the Williamses' counterclaims are within the scope of what the parties agreed to arbitrate. This is, at heart, a matter of contract interpretation. See Stolt-Nielsen S.A. v. AnimalFeeds Int'l Corp. , 559 U.S. 662 , 682, 130 S.Ct. 1758 , 176 L.Ed.2d 605 (2010). The relevant portion of the parties' fee agreement provides:

FEE ON TERMINATION. If Client terminates Firm's employment before conclusion of the case without good cause, Client shall pay Firm a fee and expenses based on the fair and reasonable value of the services performed by Firm before termination. If any disagreement arises about the termination fee, the client may choose two persons from a service profession, and the firm may choose one person. The firm will be bound by a majority decision of the three persons as to a fair fee. If the Firm terminates the representation, then it shall receive no fee or expenses.

This provision is narrow, so all we need to do is determine whether the agreement, reasonably read, "cover[s] the dispute[s] at hand." Lipton-U. City, LLC v. Shurgard Storage Ctrs., Inc. , 454 F.3d 934 , 937 (8th Cir. 2006) ; see also 3M Co. v. Amtex Sec., Inc. , 542 F.3d 1193 , 1198-99 (8th Cir. 2008) (discussing the treatment of broad arbitration clauses and how they differ from narrower ones).

Under the contract, the obligation to arbitrate applies to "disagreement[s] ... about the termination fee." A disagreement about the termination fee means a dispute about what fee, if any, the firm is entitled to receive for its work. The counterclaims the district court enjoined do not fit this definition. Rather than seeking to establish that the Williamses should pay a lower fee than the firm requested, or no fee at all, the counterclaims seek an award of damages from the firm. Those counterclaims that remain in the arbitration, by contrast, generally do not. Rather, they invoke the firm's alleged misconduct as a basis to deny a termination fee altogether or to reduce the amount the Williamses owe. 2

To allow all the counterclaims to proceed to arbitration, as the Williamses urge, would be inconsistent with the parties' agreement. The Williamses emphasize that their claims are "based on" their fee dispute with the firm and arise out of the same underlying facts. But the language in the agreement is narrow; it requires arbitration only of disagreements about the termination fee, not disputes arising out of or "based on" a fee dispute.

The Williamses also insist that the district court should have ignored the remedies they requested in deciding the arbitrability question. According to the Williamses, what remedies are available is a question for the arbitrators, not the court. Cf. Benihana, Inc. v. Benihana of Tokyo, LLC , 784 F.3d 887 , 899 (2d Cir. 2015) ("[W]hen the parties have agreed to submit a dispute to arbitration, a court may [not] enjoin a party from seeking a particular remedy in arbitration [even] if, in the court's assessment, that remedy would have no basis in the parties' agreement."). It is true that arbitrability generally does not depend on the remedy sought, but that is because arbitration clauses, especially broad ones, often do not say anything about the available remedies. But here, the fee agreement ties arbitration to a particular remedy available to the firm: recovery of the termination fee. So it is logical-indeed, necessary-to determine what the counterclaims seek. If what they seek is to reduce or eliminate the money the Williamses owe to the firm, the claims are arbitrable; if they seek something else-like money from the firm-they are not.

We do agree with the Williamses on one point, though. Before reaching the question of whether the counterclaims were arbitrable, the district court should not have decided that the Williamses terminated the relationship. This finding established one of the two conditions for the firm to recover a termination fee, the other being that the termination was not for good cause. Yet the fee agreement treats both conditions identically. So when the court recognized that the question of good cause was for the arbitrators to decide, it should have reached the same conclusion about the termination question.

III.

We affirm the district court, except its finding that the Williamses, not the firm, terminated the representation, and remand for further proceedings.