How bad is it that we lose compositionality? It is generally agreed that some of the standard arguments for compositionality are not particularly compelling. In particular, we don’t need compositionality to explain why people can understand an indefinite number of sentences, and we don’t need it for explaining how languages can be learned. To explain such facts, it suffices that there is some procedure for establishing the meanings of sentences, but it is not strictly necessary for this procedure to be compositional. Compositionality is often viewed as a methodological principle (Groenendijk and Stokhof 1989, 1991; Janssen 1997; Dever 1999), since any model of interpretation can be made compositional if we are sufficiently relaxed about the nature of lexical meanings and/or the syntactic structures over which the compositional theory is defined. In the case of DRT, the standard approaches to making the system compositional involve dispensing with Kamp’s construction algorithm, and replacing it with a system in which DRSs can be composed either through suitable merge operations (Zeevat 1989b), or, in dynamic semantic systems like those of Groenendijk and Stokhof (1989) and Muskens (1996), through use of function application in a lambda calculus. But while most such systems capture meanings for sentences that are closely related to those of original DRT, they do not capture every aspect of DRT. In particular, whereas anaphora resolution is an integral part of DRT, in compositional theories anaphora resolution is assumed to be performed by a separate component of the theory.