Is federal diversity jurisdiction case-specific or claim-specific? Consider a state-law case in federal court between a Texas plaintiff and two defendants—one from California and the other from Texas. The complete-diversity rule taught to every first-year law student makes clear that, when the diversity defect is noted, the court lacks subject-matter jurisdiction over the action as a whole. The court cannot, therefore, proceed with either claim as long as the nondiverse claim remains. But does the court’s subject-matter jurisdiction nevertheless extend to the diverse claim, such that the case can continue if the spoiler is dismissed? This question is both pervasive and unsettled. We identify and explore two possible answers, each based on a different theory of subject-matter jurisdiction. The first we denote “joint jurisdiction”—an all-or-nothing theory—under which the presence of a nondiverse claim contaminates the whole case and deprives the court of diversity jurisdiction over diverse claims. The second we denote “several jurisdiction”—a claim-by-claim theory—under which the court lacks subject-matter jurisdiction over the nondiverse claim but always had, and continues to have, diversity jurisdiction over the diverse claim. We show that each theory boasts jurisprudential support, leaving the doctrine ambivalent on a question that affects thousands of cases filed in federal court each year. We then offer a way to reconcile these seemingly incompatible theories and precedent: manipulation of the nonjurisdictional time-of-filing rule. Finally, we discuss how that solution potentially creates new tensions, particularly regarding the notion that a court without subject-matter jurisdiction over an action may nonetheless render a binding adjudication of claims within that action.