Before KING, SMITH, and HAYNES, Circuit Judges. JERRY E. SMITH, Circuit Judge: Federal courts can enforce an arbitration agreement only if they could hear the underlying “controversy between the parties.” 9 U.S.C. § 4. In Vaden v. Discover Bank, 556 U.S. 49 (2009), the Court told us to define that “controversy” by looking to the whole dispute, including any state-court pleadings. The question here is whether we must define the “parties” that way, too. Because the statute makes clear that we may not, we vacate the dismissal and remand. I. Telesforo Aviles worked for ADT, L.L.C., installing security systems in customers’ homes. After a decade of service, Aviles began spying on customers using the cameras he had installed. ADT discovered Aviles’s misconduct, fired him, and reported him to the authorities. But by then, Aviles had spied on more than two hundred customers, accessing some accounts hundreds of times. Kamala Richmond and her family are citizens of Texas. They say they were among Aviles’s victims. After Aviles’s conduct became known, the Richmonds sued Aviles and ADT in Texas state court on sundry state-law claims, seeking more than $1 million in damages. But the Richmonds’ contract with ADT contained an arbitration clause. To enforce that clause, ADT brought this federal suit under § 4 of the Federal Arbitration Act. ADT premised jurisdiction on the complete diversity between the Richmonds and ADT, which is a citizen of Florida and Delaware. A federal court can hear a suit to compel arbitration only if it could hear “a suit arising out of the controversy between the parties.” 9 U.S.C. § 4. To define that “controversy,” a federal court must “look through” the § 4 petition “to the parties’ underlying substantive controversy.” Vaden, 556 U.S. at 62. If a federal court could hear a suit arising from that “whole controversy,” id. at 67, then that court can hear the § 4 suit, id. at 70. Applying Vaden, the district court looked through ADT’s federal suit to the Richmonds’ state-court complaint, which named Aviles and ADT as defendants. From that, the court concluded that the “whole controversy” included Aviles, ADT, and the Richmonds. But those parties lacked diversity of citizenship because Aviles, like the Richmonds, is from Texas. See 28 U.S.C. § 1332(a)(1). On that ground, the court dismissed ADT’s suit for want of diversity jurisdiction. ADT asks us to revive its suit. ADT says that Vaden doesn’t extend to diversity of citizenship and that every federal circuit to consider the question agrees. The Richmonds acknowledge the weight of opposing authority but contend that Vaden requires affirmance. Although neither side stresses § 4′s text, it resolves this case. II. Vaden tells us to look to the “whole controversy,” not just the petition to compel arbitration, to define the controversy over which the petition asserts federal jurisdiction. See Vaden, 556 U.S. at 67. The district court went a step further: It applied Vaden‘s look-through test to define the “parties” to that controversy. That was error, so we vacate the dismissal and remand. A. Section 4 is clear: The only controversy that bears on our jurisdiction is “the controversy between the parties.” 9 U.S.C. § 4 (emphasis added). Those “parties” are only the parties to the suit to compel arbitration. Section 4 empowers [a] party aggrieved by the alleged failure, neglect, or refusal of another to arbitrate under a written agreement for arbitration [to] petition any United States district court which, save for such agreement, would have jurisdiction under title 28, in a civil action or in admiralty of the subject matter of a suit arising out of the controversy between the parties, for an order directing that such arbitration proceed in the manner provided for in such agreement. Id. (emphasis added). Beyond the quoted excerpt, the word “party” or “parties” appears at six other points in § 4. At all those points, § 4 refers to one or both of two parties. The first are those who “fail[ ], neglect, or refus[e] . . . to arbitrate under a written agreement for arbitration.” Id. The second are those whom the first aggrieve by not submitting to arbitration. See id. In other words, § 4 uses “parties” to mean only the parties to the § 4 suit: those who refuse to abide their agreement to arbitrate and those whom they aggrieve by doing so. Nonparties to that suit do not matter. Reading “parties” more broadly would make no textual sense. To take one example, if “the making of the agreement for arbitration . . . is not in issue,” a court must “order . . . the parties to proceed to arbitration.” Id. That provision applies easily to those who have agreed to arbitrate. But how could it apply to nonparties? A court can’t compel a party to arbitrate when it never agreed to. See Moses H. Cone Mem’l Hosp. v. Mercury Constr. Corp., 460 U.S. 1, 19–20 (1983). Vaden does not control. There, the Court explained only how we must define the § 4 “controversy.” It never defined the “parties” whom § 4 describes. Vaden‘s facts show why. Vaden was a federal-question case. See Vaden, 556 U.S. at 70. And unlike diversity jurisdiction, federal-question jurisdiction turns not on the identity of the parties but on the subject matter of the controversy.[1] Even if the Vaden Court could have decided who the “parties” are, it did not. Vaden spoke only to the word “controversy.” Section 4, the Court explained, “does not invite federal courts to dream up counterfactuals when actual litigation has defined the parties’ controversy.” Vaden, 556 U.S. at 68 (emphasis added). “The relevant question,” the majority persisted, “is whether the whole controversy between the parties—not just a piece broken off from that controversy—is one over which the federal courts would have jurisdiction.” Id. at 67 (emphasis added). The majority even framed the question presented as whether “a district court, if asked to compel arbitration pursuant to § 4, [should] ‘look through’ the petition and grant the requested relief if the court would have federal-question jurisdiction over the underlying controversy.” Id. at 53 (emphasis added). Although Vaden did not define “parties,” both its language and its method support our reading. After looking to § 4′s text, the Court opined that it refers only to the two parties we’ve identified: the party “seek[ing] arbitration pursuant to a written agreement” and the party who “resists.” Id. at 62. And though Vaden drew a partial dissent, every Justice agreed that the Court’s task was to interpret § 4′s text.[2] We do likewise, drawing the meaning of “parties” directly from that section. Moses H. Cone also favors our view. Moses Cone Hospital, a North Carolina citizen, had contracted with Mercury, an Alabama citizen. The contract contained an arbitration clause. Rather than arbitrate, the hospital sued Mercury and a North Carolina architect, who hadn’t signed the agreement to arbitrate, in state court. Mercury then moved in federal court to compel arbitration on diversity-of-citizenship grounds. Moses H. Cone, 460 U.S. at 7. The federal district court stayed Mercury’s suit, citing the state proceedings. Id. The Court in Moses H. Cone considered only the appealability and propriety of the district court’s stay, not jurisdiction. Id. at 8. But if the Richmonds were right that the FAA requires federal courts to determine the “parties” from the first-filed state-court complaint, the Court should have dismissed[3] because the architect’s inclusion in the hospital’s state-court suit destroyed complete diversity. See Moses H. Cone, 460 U.S. at 7 n.4. The Court instead affirmed the Fourth Circuit’s decision to reverse the stay and to remand. Id. at 29. The Court passed over the jurisdictional question, leaving untouched the Fourth Circuit’s forceful holding that diversity jurisdiction was proper.[4] Other circuits agree that we must determine diversity of citizenship in a § 4 suit from the parties to that suit. In Hermès of Paris, Inc. v. Swain, 867 F.3d 321 (2d Cir. 2017), the court observed that § 4′s text refers only to “the parties to the petition to compel arbitration.” Id. at 326; see also Doctor’s Assocs. v. Distajo, 66 F.3d 438, 445 (2d Cir. 1995) (“The ‘parties’ to which § 4 of the FAA refers are the parties to the petition to compel.”). On that ground, the court rejected the claim that courts must look through the § 4 petition to determine who the parties are. Swain, 867 F.3d at 325–26. The Eighth Circuit has agreed,[5] noting that every circuit precedent before Vaden had looked “only to the citizenship of the parties to the [§ 4] action.” Rutherford, 605 F.3d at 489.[6] Reading “parties” to mean only the parties to the § 4 petition also advances the core policy behind the look-through test. Vaden stressed that looking only to a § 4 petition to define the parties’ controversy would invite litigants to manipulate federal jurisdiction. See Vaden, 556 U.S. at 66–70. The look-through test defeats artful pleading by ensuring that federal jurisdiction over a petition to compel arbitration corresponds with federal jurisdiction over the parties’ actual dispute. Likewise, uncritically crediting how the first litigant defines the parties, as the Richmonds suggest, would invite “[a]rtful dodges” of federal jurisdiction. Id. at 67. After agreeing to arbitrate its claims against a diverse defendant, a party could breach that compact, sue in state court, and join a nondiverse nonparty to its suit to deprive federal courts of the power to hold it to its bargain. The Richmonds’ rule also would trap those seeking to enforce arbitration agreements between a rock and a hard place: If they move early to compel arbitration, beating a state-court filing, the dispute may be unripe. See, e.g., ADT LLC v. Madison, No. 3:20-CV-1417, 2020 WL 7046850, at *4 (N.D. Tex. Nov. 30, 2020). But if they wait until after the plaintiff has filed a state-court complaint, that plaintiff may defeat federal jurisdiction by suing a nondiverse nonparty. Allowing that tactic would “fatally undermine the FAA,” Swain, 867 F.3d at 324 (cleaned up), and cheapen the power of this court. Section 4 defines “parties” as it does to bar litigants from abusing federal jurisdiction. Having agreed to arbitrate its claims against a diverse defendant, a plaintiff may not escape our power by joining to its state-court suit nondiverse persons whom it could not hale into arbitration. “Parties,” in § 4, means the parties to the § 4 suit—not everyone against whom one party claims relief. B. We have diversity jurisdiction here. The amount in controversy far exceeds $75,000. Complete diversity exists as well. The parties to the § 4 petition are ADT and the Richmonds. The Richmonds sued Aviles, too. But only the Richmonds and ADT are alleged to have agreed to arbitrate,[7] and only they are the parties to ADT’s suit. One wrinkle remains. An indispensable party is one whose joinder is vital to avoid serious prejudice to that person or the parties already joined. See FED. R. CIV. P. 19(b) (listing the relevant factors). If Aviles is indispensable to the dispute between ADT and the Richmonds, diversity jurisdiction may not be proper. See, e.g., Brown v. Pac. Life Ins. Co., 462 F.3d 384, 393–94 (5th Cir. 2006); see also Rutherford, 605 F.3d at 491. On remand, the district court should decide whether Aviles could be indispensable to an arbitral proceeding to which he never agreed.[8] C. The Richmonds protest that Vaden instructs us to look to the “substantive controversy as the parties have framed it.” Volvo Trucks N. Am., Inc. v. Crescent Ford Truck Sales, Inc., 666 F.3d 932, 937 (5th Cir. 2012). By listing Aviles in their state-court complaint, the Richmonds say, they framed that controversy to include him, so there is no diversity jurisdiction here. We disagree. The statute says otherwise. Section 4 doesn’t tell us to look to any controversy. It points us only to the controversy “between the parties” to the § 4 suit. The Richmonds’ approach would erase that qualifying phrase. Vaden‘s look-through test requires us to define the § 4 “controversy” by looking to the whole dispute “between the parties.” The Richmonds say their framing of who the parties are is part of that controversy. But that can’t be right. “Between the parties” qualifies the “controversy”; it cannot be that controversy. Wherever possible, we must read statutes to give effect to their every word.[9] If the word “parties” were, as the Richmonds suggest, a mere subset of the “controversy” that § 4 describes, then the FAA’s drafters would not have written “between the parties” at all. We won’t declare that phrase surplusage; it is neither unclear nor absurd.[10] There is no injustice in refusing to credit the Richmonds’ state-court complaint as the definitive statement of the parties to the dispute. Suppose that we struck the words “between the parties” from § 4. We still would have to look to the whole dispute as framed by the parties. And the Richmonds framed that dispute, in no small part, by agreeing to arbitrate with ADT and ADT only. When a party agrees to arbitrate a dispute with another, it consents to resolving that dispute separately from others, even if piecemeal litigation results. See Moses H. Cone, 460 U.S. at 20. The party may not defeat federal jurisdiction over that dispute by sparking others that arbitration can’t resolve. * * * * * Not all is lost for the Richmonds. Perhaps the agreement to arbitrate is invalid, as they argued at the district court. We take no view on that issue. But a federal court can decide it. Because there’s diversity jurisdiction over ADT’s suit to compel arbitration, we VACATE the judgment of dismissal and REMAND. The district court shall decide whether Aviles is indispensable to this federal suit. We place no limitations on what matters the district court may address on remand in accord with this opinion. HAYNES, Circuit Judge, concurring in the judgment: I concur in the judgment of this court but would arrive there on a shorter road: the “look through” test of Vaden does not apply to diversity jurisdiction cases. See, e.g., Northport Health Servs. of Arkansas, LLC v. Rutherford, 605 F.3d 483, 491 (8th Cir. 2010); Hermes of Paris, Inc. v. Swain, 867 F.3d 321, 324-26 (2d Cir. 2017). Thus, we simply “look at” the parties to the federal litigation where there is, undoubtedly, complete diversity (though I agree with the point about “indispensable parties” being a consideration on remand). Accordingly, I concur in the judgment only.