The Joint Probability Model proposed by Marcu and Wong (2002) provides a probabilistic framework for modeling phrase-based statistical machine transla- tion (SMT). The model’s usefulness is, however, limited by the computational complexity of estimating parameters at the phrase level. We present a method of constraining the search space of the Joint Probability Model based on statistically and linguistically motivated word align- ments. This method reduces the complexity and size of the Joint Model and allows it to display performance superior to the standard phrase-based models for small amounts of training material.