It is generally assumed that ellipsis requires parallelism between the clause containing the ellipsis and some antecedent clause. We argue that the parallelism requirement generated by ellipsis must be applied in accordance with discourse structure: a matching antecedent clause must be found that locally c‐commands the clause containing the ellipsis in the discourse tree. We show that this claim makes several correct predictions concerning the interpretation of ellipsis, both in terms of the selection of the antecedent (in sluicing and verb phrase ellipsis), and in terms of the possible readings assuming a particular antecedent (in the ‘many‐clause’ puzzle and in antecedent‐contained deletion).