Phonological rules create alternations in the phonetic realizations of related words. These rules must be learned by infants in order to identify the phonological inventory, the morphological structure, and the lexicon of a language. Recent work proposes a computational model for the learning of one kind of phonological alternation, allophony (Peperkamp, Le Calvez, Nadal, & Dupoux, 2006). This paper extends the model to account for learning of a broader set of phonological alternations and the formalization of these alternations as general rules. In Experiment 1, we apply the original model to new data in Dutch and demonstrate its limitations in learning nonallophonic rules. In Experiment 2, we extend the model to allow it to learn general rules for alternations that apply to a class of segments. In Experiment 3, the model is further extended to allow for generalization by context; we argue that this generalization must be constrained by linguistic principles.