In this paper, we propose Context-Free Subphrase Grammars, a grammar formalism that is as powerful as Chomsky’s Context-Free Grammars, but without their notorious lack of modularity. The key to this improvement is an alternative approach to precedence that naturally applies to arbitrary production rules using a notion of subphrase structure. We provide evidence that our formalism is complete and sound with respect to Context-Free Grammars, and demonstrate how it can be used to define syntax in a modular way by means of a small example.