Since Bowers 1993, it has been accepted that nonverbal small clauses are headed by a functional head, Pred0, whose function is to obligatorily mediate all nonverbal predication. I argue against this hypothesis by critically reanalyzing the original syntactic arguments for PredP, examining possible semantic support for mediated predication, and reviewing the putative crosslinguistic evidence for overt equivalence of Pred0. I first demonstrate that the facts originally taken as motivating a functional head in small clauses can now be accounted for by independently needed assumptions. I then show that standard Montagovian semantics treating NPs, APs, and PPs as unsaturated functions requires no mediating projection and that suggested alternative meanings for Pred0 either fail or cannot be used as motivation for its existence. Finally, I provide evidence that the syntax of copular particles and other “overt predicators” is different from that expected of Pred0 in such ways that they cannot be taken as prima facie evidence for it either. I sketch an alternative theory linking the use of predicative particles to nominal predication and provide evidence for it from crosslinguistic lexicalization patterns of copular particles. In sum, neither theoretical nor empirical considerations require a mediating functional head in small clauses, and therefore the PredP hypothesis should be abandoned.