Most statistical machine translation systems rely on composed rules (rules that can be formed out of smaller rules in the grammar). Though this practice improves translation by weakening independence assumptions in the translation model, it nevertheless results in huge, redundant grammars, making both training and decoding inefficient. Here, we take the opposite approach, where we only use minimal rules (those that cannot be formed out of other rules), and instead rely on a rule Markov model of the derivation history to capture dependencies between minimal rules. Large-scale experiments on a state-of-the-art tree-to-string translation system show that our approach leads to a slimmer model, a faster decoder, yet the same translation quality (measured using BLEU) as composed rules.