This paper discusses how to give an analysis of secondary predication structures within a compositional semantic theory. There are two basic options for analysing secondary predicates compositionally. One is to treat them as direct predication structures within a small clause and the other is to analyse them as forming complex predicates together with the matrix verb at the VP level. We compare these approaches, showing that depictives and circumstantials (which we analyse as depictives under the scope of a modal operator) have a plausible compositional interpretation only under the complex predicate approach. Resultative secondary predicates can in principle be analysed either way. However, we suggest the complex predicate account is preferable for two reasons: (i) the small clause account assumes a lexical relation between the matrix verb and the small clause, and this lexical relation is elusive and difficult to specify; (ii) the complex predicate account allows an explanation of why depictives and resultatives are the only two kinds of secondary predicates semantically available. We show that on the complex predicate account, the semantic range of available secondary predicates follows from general constraints on event structure.