We present a novel approach to word reordering which successfully integrates syntactic structural knowledge with phrase-based SMT. This is done by constructing a lattice of alternatives based on automatically learned probabilistic syntactic rules. In decoding, the alternatives are scored based on the output word order, not the order of the input. Unlike previous approaches, this makes it possible to successfully integrate syntactic reordering with phrase-based SMT. On an English-Danish task, we achieve an absolute improvement in translation qual