Statistical MT has made great progress in the last few years, but current translation models are weak on re-ordering and target language fluency. Syntactic approaches seek to remedy these problems. In this paper, we take the framework for acquiring multi-level syntactic translation rules of (Galley et al., 2004) from aligned tree-string pairs, and present two main extensions of their approach: first, instead of merely computing a single derivation that minimally explains a sentence pair, we construct a large number of derivations that include contextually richer rules, and account for multiple interpretations of unaligned words. Second, we propose probability estimates and a training procedure for weighting these rules. We contrast different approaches on real examples, show that our estimates based on multiple derivations favor phrasal re-orderings that are linguistically better motivated, and establish that our larger rules provide a 3.63 BLEU point increase over minimal rules.