This work is concerned with the space of alignments searched by word alignment systems. We focus on situations where word re-ordering is limited by syntax. We present two new alignment spaces that limit an ITG according to a given dependency parse. We provide D-ITG grammars to search these spaces completely and without redundancy. We conduct a careful comparison of five alignment spaces, and show that limiting search with an ITG reduces error rate by 10%, while a D-ITG produces a 31% reduction. .
