A well‐established principle of language is that there is a preference for closely related words to be close together in the sentence. This can be expressed as a preference for dependency length minimization (DLM). In this study, we explore quantitatively the degree to which natural languages reflect DLM. We extract the dependencies from natural language text and reorder the words in such a way as to minimize dependency length. Comparing the original text with these optimal linearizations (and also with random (...) linearizations) reveals the degree to which natural language minimizes dependency length. Tests on English data show that English shows a strong effect of DLM, with dependency length much closer to optimal than to random; the optimal English grammar also has many specific features in common with English. In German, too, dependency length is significantly less than random, but the effect is much weaker than in English. We conclude by speculating about some possible reasons for this difference between English and German. (shrink)