Modal dispositionalism is the view that possibilities are a matter of the dispositions of individual objects: it is possible that p if and only if something has a disposition for p to be the case. We raise a problem for modal dispositionalism: nothing within the theory rules out that there could be necessary, perfect masks, which make the manifestation of a disposition impossible. Unless such necessary perfect masks are ruled out, modal dispositionalism runs the risk of failing to provide a sufficient condition for possibility, and indeed of engendering contradictions. But to rule them out, modal dispositionalism would have to revise a crucial tenet of the view, its localism.