Children are facile at both discovering word boundaries and using those words to build higher-level structures in tandem. Current research treats lexical acquisition and grammar induction as two distinct tasks; doing so has led to unreasonable assumptions. State-ofthe-art unsupervised results presuppose a perfectly segmented, noise-free lexicon, while largely ignoring how the lexicon is used. This paper combines both tasks in a novel framework for bootstrapping lexical acquisition and grammar induction.