We propose a robust answer reranking model for non-factoid questions that integrates lexical semantics with discourse information, driven by two representations of discourse: a shallow representation centered around discourse markers, and a deep one based on Rhetorical Structure Theory. We evaluate the proposed model on two corpora from different genres and domains: one from Yahoo! Answers and one from the biology domain, and two types of non-factoid questions: manner and reason. We experimentally demonstrate that the discourse structure of nonfactoid answers provides information that is complementary to lexical semantic similarity between question and answer, improving performance up to 24% (relative) over a state-of-the-art model that exploits lexical semantic similarity alone. We further demonstrate excellent domain transfer of discourse information, suggesting these discourse features have general utility to non-factoid question answering.