We achieve significant improvements in several syntax-based machine translation experiments using a string-to-tree variant of multi bottom-up tree transducers. Our new parameterized rule extraction algorithm extracts string-to-tree rules that can be discontiguous and non-minimal in contrast to existing algorithms for the tree-to-tree setting. The obtained models significantly outperform the string-to-tree component of the Moses framework in a large-scale empirical evaluation on several known translation tasks. Our linguistic analysis reveals the remarkable benefits of discontiguous and non-minimal rules.