Multiword expressions (MWEs) pose a problem for lexicalist theories like Lexical Functional Grammar (LFG), since they are prima facie counterexamples to a strong form of the lexical integrity principle, which entails that a lexical item can only be realised as a single, syntactically atomic word. In this paper, I demonstrate some of the problems facing any strongly lexicalist account of MWEs, and argue that the lexical integrity principle must be weakened. I conclude by sketching a formalism which integrates a Tree Adjoining Grammar into the LFG architecture, taking advantage of this relaxation.