Word alignment methods can gain valuable guidance by ensuring that their alignments maintain cohesion with respect to the phrases specified by a monolingual dependency tree. However, this hard constraint can also rule out correct alignments, and its utility decreases as alignment models become more complex. We use a publicly available structured output SVM to create a max-margin syntactic aligner with a soft cohesion constraint. The resulting aligner is the first, to our knowledge, to use a discriminative learning method to train an ITG bitext parser.