Many different topic models have been used successfully for a variety of applications. However, even state-of-the-art topic models suffer from the important flaw that they do not capture the tendency of words to appear in bursts; it is a fundamental property of language that if a word is used once in a document, it is more likely to be used again. We introduce a topic model that uses Dirichlet compound multinomial (DCM) distributions to model this burstiness phenomenon. On both text and non-text datasets, the new model achieves better held-out likelihood than standard latent Dirichlet allocation (LDA). It is straightforward to incorporate the DCM extension into topic models that are more complex than LDA.