Recent research has shown clear improvement in translation quality by exploiting linguistic syntax for either the source or target language. However, when using syntax for both languages (“tree-to-tree” translation), there is evidence that syntactic divergence can hamper the extraction of useful rules (Ding and Palmer 2005 ). Smith and Eisner ( 2006 ) introduced quasi-synchronous grammar, a formalism that treats non-isomorphic structure softly using features rather than hard constraints. Although a natural fit for translation modeling, its flexibility has proved challenging for building real-world systems. In this article, we present a tree-to-tree machine translation system inspired by quasi-synchronous grammar. The core of our approach is a new model that combines phrases and dependency syntax, integrating the advantages of phrase-based and syntax-based translation. We report statistically significant improvements over a phrase-based baseline on five of seven test sets across four language pairs. We also present encouraging preliminary results on the use of unsupervised dependency parsing for syntax-based machine translation.