Taking as starting-point Maria Tymoczko’s claim (1999) that syntagmatic elements in texts present the greatest challenges to translators and readers of translations, this paper argues that literary translators and translation scholars need to pay greater attention to clusters of wordplay rather than distinguishing puns as individual, separate brain-teasers. Hence, more is at stake in the translation of wordplay than just trying to transfer the source text complexities into the target language. Historical, social and other contextual and intertextual factors must also be taken into consideration. My case in point is an examination of the transfer of highly challenging networks of puns in James Joyce’s Ulysses (1922) into Danish and German. The theoretical frame of reference is a discussion of puns in the critical works of Dirk Delabastita, Jonathan Culler, Derek Attridge and Patricia Parker followed by a critique of translator and critic Frank Heibert’s methods of evaluating the German translations.