Abstract: We propose a simple training regime that can improve the extrinsic performance of a parser, given only a corpus of sentences and a way to automatically evaluate the extrinsic quality of a candidate parse. We apply our method to train parsers that excel when used as part of a reordering component in a statistical machine translation system. We use a corpus of weakly-labeled reference reorderings to guide parser training. Our best parsers contribute significant improvements in subjective translation quality while their intrinsic attachment scores typically regress.