One of the most astonishing features of human language is its capacity to convey information efficiently in context. Many theories provide informal accounts of communicative inference, yet there have been few successes in making precise, quantitative predictions about pragmatic reasoning. We examined judgments about simple referential communication games, modeling behavior in these games by assuming that speakers attempt to be informative and that listeners use Bayesian inference to recover speakers’ intended referents. Our model provides a close, parameter-free fit to human judgments, suggesting that the use of information-theoretic tools to predict pragmatic reasoning may lead to more effective formal models of communication.