Across many unrelated languages, conjunctions are known to allow for conditional readings (e.g. `You sing another song and I'm out of here’ for roughly `If you sing another song, I'm out of here.'). Similar effects are found for a variety of first conjunct form types (`Sing another song/One more song/You only have to sing another song..') and also in the absence of an overt conjunction (`You sing. I leave.'). The resulting conditionals typically express generic or predictive readings and seem to exclude epistemic conditionals. I show that this constraint is better understood as pertaining to discourse structure rather than modal flavor. Building on Kaufmann & Whitman (under review), I adduce crosslinguistic evidence that conditional readings result from regular coordinations under topicalization of the first coordinand, and I provide an analysis in a dynamic logic with propositional discourse referents. Finally, I explore whether the restriction on possible readings could result from the topicalization operation involved being always contrastive.