Case competition is a phenomenon which arises when a noun is assigned two cases. Grammars tend to resolve the situation by eliminating one of the two cases. The talk investigates the peculiarities that accompany this process in two varieties of Ossetic (Iron and Digor). I argue that the facts are best understood if case competition is nothing else but ellipsis under c-command and identity. As a consequence, the notion of case competition is eliminated from the grammar at the level of underlying mechanisms, and its effects are subsumed under the theory of ellipsis.