The idea that quotidian, middle-level concepts typically have internal structure-definitional, statistical, or whatever—plays a central role in practically every current approach to cognition. Correspondingly, the idea that words that express quotidian, middle-level concepts have complex representations "at the semantic level" is recurrent in linguistics; it is the defining thesis of what is often called "lexical semantics," and it unites the generative and interpretive traditions of grammatical analysis. Hale and Keyser (HK) (1993) have endorsed a version of lexical decomposition according to which "denominal" verbs are typically derived from phrases containing the corresponding nouns: ‘singvtr’ is supposed to come from something like DO A SONG; ‘saddlevtr’ is supposed to come from something like PUT A SADDLE ON; ‘shelvevtr’ is supposed to come from something like PUT ON A SHELF; and so forth. Their case for these claims revives a form of argument, the "impossible-word" argument, which has for some time been in eclipse. In this article we will claim that, whatever the right account of lexical decomposition eventually turns out to be, impossible-word arguments are infirm and should be discounted. We will use HK's paper as a text for this critique.