Model minimization has been shown to work well for the task of unsupervised part-of-speech tagging with a dictionary. In (Ravi and Knight, 2009), the authors invoke an integer programming (IP) solver to do model minimization. However, solving this problem exactly using an integer programming formulation is intractable for practical purposes. We propose a novel two-stage greedy approximation scheme to replace the IP. Our method runs fast, while yielding highly accurate tagging results. We also compare our method against standard EM training, and show that we consistently obtain better tagging accuracies on test data of varying sizes for English and Italian.