We formulate a new generalization of the distribution of ellipsis remnants. Ellipsis cannot strand functional material to the exclusion of a potential prosodic host (the Stranding Generalization). Explaining the Stranding Generalization requires a theory of ellipsis in which the prosodic needs of ellipsis remnants can be taken into account. Drawing on Match Theory (Selkirk2009, Selkirk2011), we develop an account which locates the computation of ellipsis in the syntax-prosody mapping. Specifically, ellipsis results from an optional reranking of a constraint (DestressGiven), which forces reduction of semantically recoverable material, over Match constraints governing the realization of syntactic elements in prosodic structure. The Stranding Generalization is shown to follow from independently motivated prosodic well-formedness constraints, which in the relevant cases cannot be reconciled with the ranking responsible for ellipsis. The broader implications of our analysis, if successful, is that it motivates a view of ellipsis whereby any constraints on ellipsis beyond semantic recoverability are the result of competition between candidates for the possible phonological output of the syntactic input.