This paper examines a particular case of embedded pragmatic effect, here dubbed "local pragmatic enrichment". I argue that local enrichment is fairly easily accommodated within semantic theories which take content to be structured. Two standard approaches to dynamic semantics, DRT and Heimian CCS, are discussed as candidates. Focusing on cases of local enrichment of disjuncts in clausal disjunctions, I point out that in these cases, local enrichment is driven by global felicity requirements, demonstrating that the local/global distinction is not a simple dichotomy.