Automatic word alignment is a key step in training statistical machine translation systems. Despite much recent work on word alignment methods, alignment accuracy increases often produce little or no improvements in machine translation quality. In this work we analyze a recently proposed agreement-constrained EM algorithm for unsupervised alignment models. We attempt to tease apart the effects that this simple but effective modiﬁcation has on alignment precision and recall trade-offs, and how rare and common words are affected across several language pairs. We propose and extensively evaluate a simple method for using alignment models to produce alignments better-suited for phrase-based MT systems, and show signiﬁcant gains (as measured by BLEU score) in end-to-end translation systems for six languages pairs used in recent MT competitions.