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Mixtures of Polya tree models provide a flexible alternative when a parametric model may only hold approximately. I provide computational strategies for obtaining full semiparametric inference for mixtures of finite Polya tree models given a standard parameterization, including models that would be troublesome to fit using Dirichlet process mixtures. Recommendations are put forth on choosing the level of a finite Polya tree, and model comparison is discussed. Several examples demonstrate the utility of finite Polya tree modeling, including data fit to generalized linear mixed models and several survival models.