A number of authors have recently used causal models to develop a promising semantics for non-backtracking counterfactuals. Briggs (Philosophical Studies 160:39–166, 2012) shows that when this semantics is naturally extended to accommodate right-nested counterfactuals, it invalidates modus ponens, and therefore violates weak centering given the standard Lewis/Stalnaker interpretation of the counterfactual in terms of nearness or similarity of worlds. In this paper, I explore the possibility of abandoning the Lewis/Stalnaker interpretation for some alternative that is better suited to accommodate the causal modeling (CM) semantics. I argue that a revision of McGee’s (The Journal of Philosophy 82:462–471, 1985) semantics can accommodate CM semantics without sacrificing weak centering, and that CM semantics can therefore be situated within a general semantics for counterfactuals that is based on the nearness or similarity of worlds.