We examine the problem of choosing word order for a set of dependency trees so as to minimize total dependency length. We present an algorithm for computing the optimal layout of a single tree as well as a numerical method for optimizing a grammar of orderings over a set of dependency types. A grammar generated by minimizing dependency length in unordered trees from the Penn Treebank is found to agree surprisingly well with English word order, suggesting that dependency length minimization has influenced the evolution of English. 1