We examine the effects of morphosyntactic marking and selectional restrictions of predicates on conceptual and grammatical animacy. We argue in favour of animacy as an ontological category with human, animate and inanimate entities representing discrete subtypes in the domain of entities. We distinguish between conceptual animacy, which is a gradient notion, and grammatical animacy, for which discrete, binary oppositions are needed. The main aim of this paper is to argue for a distinction between overt and covert type shifts in animacy. On the one hand, overt shifts are linguistic solutions to type mismatches in the grammar. Crucially, these type shifts do not involve a shift in conceptual animacy. Covert animacy shifts, on the other hand, brought about by selectional restrictions or by the linguistic context in general, do involve a proper type shift in conceptual animacy. By making explicit the relation between the gradience of conceptual and the discreteness of grammatical animacy, and by exploring the distinction between covert and overt type shifts that involve animacy, we hope to gain a deeper understanding of animacy and its effects on language.