Starting from a broad ancient definition of 'epigrams' which includes poems which are not in elegiacs, and Martial's use of Catullus 2 (written in hendecasyllables) as a model for his own epigrams (Mart. 4.14.13-4), my paper examines epigrammatic features in Catullus 2 and 3, as well as other literary affinities that can be traced in these poems. AP 7.195 and 196 (by Meleager) are important epigrammatic models for Catullus 2, and I identify major correspondences and differences between these poems, before considering another important model for Catullus 2: Sappho fr. 1. From examination of Sapphic features in Catullus 2 and 2b, my paper moves to Catullus 3, and explores its affinities with Greek epigram (in particular the epitaphs found in AP 7 and Hellenistic curse poetry). In the final section of the paper, working from Martial's references to Catullus' passer and Catullus' use of Sappho fr. 1 in Catullus 2, I consider Catullus 2 as the opening poem of a Catullan collection, and the implications that this has for our interpretation of his poetry.