Foreign-accented speech contains multiple sources of variation that listeners learn to accommodate. Extending previous findings showing that exposure to high-variation training facilitates perceptual learning of accented speech, the current study examines to what extent the structure of training materials affects learning. During training, native adult speakers of American English transcribed sentences spoken in English by native Spanish-speaking adults. In Experiment 1, training stimuli were blocked by speaker, sentence, or randomized with respect to speaker and sentence (Variable training). At test, listeners transcribed novel English sentences produced by unfamiliar Spanish-accented speakers. Listeners’ transcription accuracy was highest in the Variable condition, suggesting that varying both speaker identity and sentence across training trials enabled listeners to generalize their learning to novel speakers and linguistic content. Experiment 2 assessed the extent to which ordering of training tokens by a single factor, speaker intelligibility, would facilitate speaker-independent accent learning, finding that listeners’ test performance did not reliably differ from that in the no-training control condition. Overall, these results suggest that the structure of training exposure, specifically trial-to-trial variation on both speaker’s voice and linguistic content, facilitates learning of the systematic properties of accented speech. The current findings suggest a crucial role of training structure in optimizing perceptual learning. Beyond characterizing the types of variation listeners encode in their representations of spoken utterances, theories of spoken language processing should incorporate the role of training structure in learning lawful variation in speech.