We present a Bayesian model of the mirror image problems of linguistic productivity and reuse. The model, known as Fragment Grammar, is evaluated against several morphological datasets; its performance is compared to competing theoretical accounts including full–parsing, full–listing, and exemplar–based models. The model is able to learn the correct patterns of productivity and reuse for two very different systems: the English past tense which is characterized by a sharp dichotomy in productivity between regular and irregular forms and English derivational morphology which is characterized by a graded cline from very productive (-ness) to very unproductive (-th).