In Bare Phrase Structure, nonbranching nodes are impossible (Speas 1986, 1990, Chomsky 1995). In a model-theoretic interpretive semantics for Logical Form, theta-roles are an anachronism and the Theta Criterion a peculiar requirement (Heim and Kratzer 1998). The conjunction of these two positions means that two centrally important paradigms of facts unaccusativity and one-replacement become essentially formally untreatable on usual assumptions about category, i.e. that N° and V° are terminal nodes without any internal structure. In this paper I’ll argue that the Distributed Morphology approach to category resolves both these problems, allowing a natural and straightforward updating of the previously standard approaches to the central facts that were proposed when they were first examined. On this approach, the contentful, open-class part of any lexical item such as a noun, verb, or adjective is contributed by an acategorial Root (?), which acquires category by being merged with a particular functional head, v°, n°, a°.