The more expressive and flexible a base formalism for machine translation is, the less efficient parsing of it will be. However, even among formalisms with the same parse complexity, some formalisms better realize the desired characteristics for machine translation formalisms than others. We introduce a particular formalism, probabilistic synchronous tree-insertion grammar (PSTIG) that we argue satisfies the desiderata optimally within the class of formalisms that can be parsed no less efficiently than context-free grammars and demonstrate that it outperforms state-of-the-art word-based and phrase-based finite-state translation models on training and test data taken from the EuroParl corpus (Koehn, 2005). We then argue that a higher level of translation quality can be achieved by hybridizing our in- duced model with elementary structures produced using supervised techniques such as those of Groves et al. (2004).