We make these observations: (a) The direct embedding of a syntactic category X in itself (X-within-X) is surprisingly rare in human language, if it exists at all. (b) Indirect self-embedding (mediated by a sequence of other categories, and usually a phase boundary) systematically goes along with intensionality effects; the embedding and the embedded XP exhibit different behavior at the semantic interface. We argue that these constraints on recursion follow from the way in which single-cycle derivations organize semantic information in grammar.