Fragment answers involve a type of ellipsis that occurs in answers to questions and these answers can be hosted by the negator not (e.g. What was his motive? Not money). The central research questions for such a negative fragment answer concern what licenses the fragment, how we can obtain a sentential meaning from its non-sentential status and what its syntactic structure is. In attempting to answer these questions, there have been two main approaches: deletion-based sentential approaches and surface-oriented, direct interpretation (DI) approaches. This article first discusses attested data of such negated fragment answers that could challenge both directions and argues for a direct interpretation 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 its proper propositional meaning.