We introduce a novel semantic representation formalism, Almost Flat Functional semantics (AFF), which is designed as an intelligent compromise between linguistically motivated predicate/argument semantics and ad hoc engineering solutions based on flat feature/value lists; the central idea is to tag each semantic element with the functional marking which most closely surrounds it. We argue that AFF is well-suited for medium-vocabulary speech translation applications, and describe simple and general algorithms for parsing, generating and performing transfer using AFF representations. The formalism has been fully implemented within a medium vocabulary interlingua-based Open Source speech translation system which translates between English, French, Japanese and Arabic.