Heim's (1982, 1983b) dynamic semantics provides an attractive system for capturing the basic facts about presupposition projection. A long-standing criticism of this semantics is that it requires for each connective lexical stipulations that are not determined by its truth-conditional meaning. I give a precise formulation of this criticism in terms of what I call a" rewrite semantics". Then, I use this idea of a rewrite semantics to formulate a new version of dynamic semantics. This version does not require stipulations particular to individual connectives, but rather allows a derivation of the presupposition projection properties for each connective from its truth-conditional meaning.