Tonosyntax in the Dogon languages of Mali is characterized by word-level tone overlays that apply in specific morphosyntactic contexts. This paper focuses on the resolution of competitions that arise when a word is targeted by more than one tone overlay. For example, in Poss N Adj the possessor and the adjective compete to impose their respective tone overlays on (at least) the noun, and Dogon languages show different outcomes. We argue that overlays are tonal morphemes associated with particular syntactic positions and propose a series of phrasal Optimality Theoretic constraints, grounded in syntactic structure, that control the association of these morphemes. The relative ranking of constraints determines the outcome of tonosyntactic competitions in a given language.