In this article we use well-known machine learning methods to tackle a novel task, namely the classification of non-sentential utterances (NSUs) in dialogue. We introduce a fine-grained taxonomy of NSU classes based on corpus work, and then report on the results of several machine learning experiments. First, we present a pilot study focused on one of the NSU classes in the taxonomy—bare wh-phrases or “sluices”—and explore the task of disambiguating between the different readings that sluices can convey. We then extend the approach to classify the full range of NSU classes, obtaining results of around an 87% weighted F-score. Thus our experiments show that, for the taxonomy adopted, the task of identifying the right NSU class can be successfully learned, and hence provide a very encouraging basis for the more general enterprise of fully processing NSUs.