<p>An important component in the interventionist account of causal explanation is an interpretation of counterfactual conditionals as statements about consequences of hypothetical interventions. The interpretation receives a formal treatment in the framework of functional causal models. In Judea Pearl’s influential formulation, functional causal models are assumed to satisfy a “unique-solution” property; this class of Pearlian causal models includes the ones called recursive. Joseph Halpern showed that every recursive causal model is Lewisian, in the sense that there is a possible worlds model in David Lewis’s semantics for counterfactuals that satisfies the exact same formulas as the causal model does in a certain language. Moreover, he demonstrated that some Pearlian (non-recursive) models are not Lewisian in this sense. This raises the question about the exact contour of Lewisian causal models. We address this question in this paper, not only regarding the class of Lewisian causal models, but also regarding an important subclass, that of Stalnakerian causal models, which is closer to Pearlian models, and an important superclass of Lewisian causal models, which results from weakening a constraint imposed by Lewis known as centering, and is in a way more natural than the class of Lewisian causal models. For each of the three classes, we provide a characterization and an axiomatization. Our results have philosophically interesting consequences, especially regarding cycles of counterfactual dependence.</p>