Successful language acquisition involves generalization, but learners must balance this against the acquisition of lexical constraints. Such learning has been considered problematic for theories of acquisition: if learners generalize abstract patterns to new words, how do they learn lexically-based exceptions? One approach claims that learners use distributional statistics to make inferences about when generalization is appropriate, a hypothesis which has recently received support from Artificial Language Learning experiments with adult learners (Wonnacott, Newport, & Tanenhaus, 2008). Since adult and child language learning may be different (Hudson Kam & Newport, 2005), it is essential to extend these results to child learners. In the current work, four groups of children (6 years) were each exposed to one of four semi-artificial languages. The results demonstrate that children are sensitive to linguistic distributions at and above the level of particular lexical items, and that these statistics influence the balance between generalization and lexical conservatism. The data are in line with an approach which models generalization as rational inference and in particular with the predictions of the domain general hierarchical Bayesian model developed in Kemp, Perfors & Tenenbaum, 2006. This suggests that such models have relevance for theories of language acquisition.