Traditional approaches to word sense disambiguation (WSD) rest on the assumption that there exists a single, unambiguous communicative intention underlying every word in a document. However, writers sometimes intend for a word to be interpreted as simultaneously carrying multiple distinct meanings. This deliberate use of lexical ambiguity -- i.e., punning -- is a particularly common source of humour. In this paper we describe how traditional, language-agnostic WSD approaches can be adapted to "disambiguate" puns, or rather to identify their double meanings. We evaluate several such approaches on a manually sense-annotated corpus of English puns and observe performance exceeding that of some knowledge-based and supervised baselines.