The present paper aims to analyse the translation of puns from a relevance-theory perspective. According to such theoretical framework, the relation between a translation and its source text is considered to be based on interpretive resemblance, rather than on equivalence. The translator would try to seek optimal relevance, in such a way that he or she would use different strategies to try to recreate the cognitive effects intended by the source writer with the lowest possible processing effort on the part of the target addressee. The analysis carried out in this study is based on two tragedies by Shakespeare – namely, Hamlet and Othello – and on five Spanish and two Galician versions of those two plays. The strategies used by the translators of those versions to render sexual puns have been analysed, focusing not only on the product but also on the process. The selection of strategy is determined, among other factors, by the specific context and by the principle of relevance. In those cases in which there is a coincidence in the relation between the levels of signifier and signified across source and target language, translators normally opt to translate literally and reproduce a pun based on the same linguistic phenomenon as the source text pun and semantically equivalent to it. In the rest of the cases, the translator will have to assess what is more relevant, either content or the effect produced by the pun.