Taking examples from English and French idioms, this paper shows that not only constituent structures rules but also most syntactic rules (such as topicalization, wh-question, pronominalization .) are subject to lexical constraints (on top of syntactic, and possibly semantic, ones). We show that such puzzling phenomena are naturally handled in a 'lexJcalized' formalism such as Tree Adjoining Grammar. The extended domain of locality of TAGs also allows one to 'lexicalize' syntactic rules while defining them at the level of constituent structures. .