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In this paper I discuss weaknesses in the traditional LFG account of complex predicates and in the XLE implementation of the same. I argue that the concept of predicate composition in general, and the mechanisms required to achieve it, are problematic, but that the most problematic element is the concept of argument fusion. I show that a semantically-integrated account of complex predicate formation is possible within LFG+glue, an account which provides a simple and effective formalization of argument fusion, and which does not suffer from the weaknesses of traditional approaches.