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A weakness of standard Optimality Theory is its inability to account for grammars with free variation. We describe here the Maximum Entropy model, a general statistical model, and show how it can be applied in a constraint-based linguistic framework to model and learn grammars with free variation, as well as categorical grammars. We report the results of using the MaxEnt model for learning two different grammars: one with variation, and one without. Our results are as good as those of a previous probabilistic version of OT, the Gradual Learning Algorithm (Boersma, 1997), and we argue that our model is more general and mathematically well-motivated.