We present a phrasal inversion transduction grammar as an alternative to joint phrasal translation models. This syntactic model is similar to its flatstring phrasal predecessors, but admits polynomial-time algorithms for Viterbi alignment and EM training. We demonstrate that the consistency constraints that allow flat phrasal models to scale also help ITG algorithms, producing an 80-times faster inside-outside algorithm. We also show that the phrasal translation tables produced by the ITG are superior to those of the flat joint phrasal model, producing up to a 2.5 point improvement in BLEU score. Finally, we explore, for the first time, the utility of a joint phrasal translation model as a word alignment method.