The results of an experiment in which participants listened to words beginning with aspirated labial stops that had exaggerated voice-onset time (VOT), and then produced the same words and different words beginning with aspirated labial and dorsal stops, are reported. Compared to baseline levels, participant's VOTs were longer after listening to the VOT-lengthened stimuli. This phonetic imitation effect generalized to all words, including those beginning with a dorsal stop, though it was somewhat stronger for the words that the participants had experienced with the VOT manipulation. The results are explained with a hierarchical Bayesian model of perceptual adaptation and phonetic imitation. Listeners are hypothesized to have implicit statistical grammars that are adapted to the phonetic properties of individual speakers; these speaker-specific grammars are nested within a statistical grammar of the speech population as a whole, which is in turn nested within a universal superpopulation grammar. Knowledge about the population and application of Bayes' theorem allows listeners to make rational inferences about the phonetic properties of a new speaker, even when their experience with that speaker is limited or impoverished. Phonetic imitation in production, including generalization from one segment to another, results from a mixture of internalized phonetic grammars.