Acquiring language requires segmenting speech into individual words, and abstracting over those words to discover grammatical structure. However, these tasks can be conflicting—on the one hand requiring memorisation of precise sequences that occur in speech, and on the other requiring a flexible reconstruction of these sequences to determine the grammar. Here, we examine whether speech segmentation and generalisation of grammar can occur simultaneously—with the conflicting requirements for these tasks being over-come by sleep-related consolidation. After exposure to an artificial language comprising words containing non-adjacent dependencies, participants underwent periods of consolidation involving either sleep or wake. Participants who slept before testing demonstrated a sustained boost to word learning and a short-term improvement to grammatical generalisation of the non-adjacencies, with improvements after sleep outweighing gains seen after an equal period of wake. Thus, we propose that sleep may facilitate processing for these conflicting tasks in language acquisition, but with enhanced benefits for speech segmentation.