Consonant epenthesis is typically assumed to be part of the basic repertoire of phonological grammars. This implies that there exists some set of linguistic data for which epenthesis is the best analysis. However, a series of artificial grammar learning experiments found no evidence that learners ever selected an epenthesis analysis. Instead, phonetic and morphological biases were revealed, along with individual variation in how learners generalised and regularised their input. These results, in combination with previous work, suggest that synchronic consonant epenthesis may only emerge very rarely, as a result of a gradual accumulation of changes over time. It is argued that stored stem–allomorph pairs should be adopted as the null hypothesis in cases of potential epenthesis, and that a universal criterion is needed for rejecting this hypothesis. Such a criterion requires a formal theory of exceptions, a necessity for falsifiability in phonological theory.