BACKGROUND Time-compressed speech, a form of rapidly presented speech, is harder to comprehend than natural speech, especially for non-native speakers. Although it is possible to adapt to time-compressed speech after a brief exposure, it is not known whether additional perceptual learning occurs with further practice. Here, we ask whether multiday training on time-compressed speech yields more learning than that observed during the initial adaptation phase and whether the pattern of generalization following successful learning is different than that observed with initial adaptation only. RESULTS Two groups of non-native Hebrew speakers were tested on five different conditions of time-compressed speech identification in two assessments conducted 10-14 days apart. Between those assessments, one group of listeners received five practice sessions on one of the time-compressed conditions. Between the two assessments, trained listeners improved significantly more than untrained listeners on the trained condition. Furthermore, the trained group generalized its learning to two untrained conditions in which different talkers presented the trained speech materials. In addition, when the performance of the non-native speakers was compared to that of a group of naïve native Hebrew speakers, performance of the trained group was equivalent to that of the native speakers on all conditions on which learning occurred, whereas performance of the untrained non-native listeners was substantially poorer. CONCLUSIONS Multiday training on time-compressed speech results in significantly more perceptual learning than brief adaptation. Compared to previous studies of adaptation, the training induced learning is more stimulus specific. Taken together, the perceptual learning of time-compressed speech appears to progress from an initial, rapid adaptation phase to a subsequent prolonged and more stimulus specific phase. These findings are consistent with the predictions of the Reverse Hierarchy Theory of perceptual learning and suggest constraints on the use of perceptual-learning regimens during second language acquisition.