How exactly do learners generalise in the face of ambiguous data? While there has been a substantial amount of research studying the biases that learners employ, there has been very little work on what sorts of biases are employed in the face of data that is ambiguous between phonological generalisations with different degrees of complexity. In this article, we present the results from three artificial language learning experiments that suggest that, at least for phonotactic sequence patterns, learners are able to keep track of multiple generalisations related to the same segmental co-occurrences; however, the generalisations they learn are only the simplest ones consistent with the data.