Let serious propositional contingentism (SPC) be the package of views which consists in (i) the thesis that propositions expressed by sentences featuring terms depend, for their existence, on the existence of the referents of those terms, (ii) serious actualism—the view that it is impossible for an object to exemplify a property and not exist—and (iii) contingentism—the view that it is at least possible that some thing might not have been something. SPC is popular and compelling. But what should we say (...) about possible worlds, if we accept SPC? Here, I first show that a natural view of possible worlds, well-represented in the literature, in conjunction with SPC is inadequate. Though I note various alternative ways of thinking about possible worlds in response to the first problem, I then outline a second more general problem—a master argument—which generally shows that any account of possible worlds meeting very minimal requirements will be inconsistent with compelling claims about _mere possibilia_ which the serious propositional contingentist should accept. (shrink)