Positive as well as negative fragment answers to wh-questions consist of a non-sentential XP but convey the same propositional content as fully sentential answers (e.g., A: What do they want? B: Money. A: What was his motive? B: Not money.) Fragment answers thus display incongruous mappings from what appear to be syntactically less than sentential structures to the semantically propositional character (Ginzburg and Sag 2000, Merchant 2005, Culicover and Jackendoff 2005). The central research questions for a (negative) fragment answer concern what licenses the fragment, how we can obtain a sentential meaning from its nonsentential status, and what is its syntactic structure. In attempting to answer these questions, there have been two main approaches: deletion-based sentential approaches and surface-oriented nonsentential approaches. This talk first discusses attested corpus data of such negated fragment answers that could challenge both directions and then argues for a direct interpretation (DI) nonsentential approach in which the interpretation of (negative) fragments is achieved by discourse machinery. The suggested approach shows that once we have a system that represents structured discourse structures, we could have straightforward mapping relations from a (negated) fragment answer to a proper propositional meaning.