We present a new model for acquiring comprehensive multiword lexicons from large corpora based on competition among n -gram candidates. In contrast to the standard approach of simple ranking by association measure, in our model n -grams are arranged in a lattice structure based on subsumption and overlap relationships, with nodes inhibiting other nodes in their vicinity when they are selected as a lexical item. We show how the configuration of such a lattice can be optimized tractably, and demonstrate using annotations of sampled n -grams that our method consistently outperforms alternatives by at least 0.05 F-score across several corpora and languages.