In the context of debates about what form a theory of meaning should take, it is sometimes claimed that one cannot understand an intersective modifier-head construction (e.g., ‘pet fish’) without understanding its lexical parts. Neo-Russellians like Fodor and Lepore contend that non-denotationalist theories of meaning, such as prototype theory and theory theory, cannot explain why this is so, because they cannot provide for the ‘reverse compositional’ character of meaning. I argue that reverse compositionality is a red herring in these debates. (...) I begin by setting out some positive arguments for reverse compositionality and showing that they fail. Then I show that the principle of reverse compositionality has two big strikes against it. First, it is incompatible with all theories of meaning on the market, including the denotationalism favored by neo-Russellians. Second, it explains nothing that is not already explained by its venerable predecessor, the principle of (forward) compositionality. (shrink)