I explore the differences in the interpretation of novel veiling and concealing euphemisms from a relevance-theoretic perspective. The research shows that the relevance of a novel veiling euphemism is established (1) via the adjustment of its linguistically encoded meaning so that it communicates the meaning encoded by a dispreferred expression, which is derived as an explicature, or (2) via its linguistically encoded meaning, derived as an explicature, and the meaning encoded by a dispreferred expression, recovered as a strong implicature. By contrast, novel concealing euphemisms achieve relevance by communicating their linguistically encoded meaning, derived as an explicature, as well as a range of weak implicatures. The recovery of weakly implicit content is not essential for inferring the speaker’s meaning.