I present arguments in favor of the Uniformity Hypothesis: the hypothesis that discourse can extend syntax dependencies without conflicting with them. I consider arguments that Uniformity is violated in certain cases involving quotation, and I argue that the cases presented in the literature are in fact completely consistent with Uniformity. I report on an analysis of all examples in the Copenhagen Dependency Treebanks involving violations of Uniformity. I argue that they are in fact all consistent with Uniformity, and conclude that the CDT should be revised to reflect this.