We report on a mechanism for semantic and pragmatic interpretation that has been designed to take advantage of the generally compositional nature of semantic analysis, without unduly constraining the order in which pragmatic decisions are made. To achieve this goal, we introduce the idea of a conditional interpretation: one that depends upon a set of assumptions about subsequent pragmatic processing. Conditional interpretations are constructed compositionally according to a set of declaratively specified interpretation rules. The mechanism can handle a wide range of pragmatic phenomena and their interactions. .