This paper proposes decoupling the dependency tree from word order, such that surface ordering is not determined by traversing the dependency tree. We develop the notion of a \emph{word order domain structure}, which is linked but structurally dissimilar to the syntactic dependency tree. The proposal results in a lexicalized, declarative, and formally precise description of word order; features which lack previous proposals for dependency grammars. Contrary to other lexicalized approaches to word order, our proposal does not require lexical ambiguities for ordering alternatives.