In this paper we present extensions of the UD scheme for modern and historical German. The extensions relate in part to fundamental differences such as those between different kinds of arguments and modifiers. We illustrate the extensions with examples from the MHG data and discuss a number of MHG-specific constructions. At the current time, we have annotated a corpus of Middle High German with almost 29K tokens using this scheme, which to our knowledge is the first UD treebank for Middle High German. Inter-annotator agreement is very high: the annotators achieve a score of α = 0.85. A statistical analysis of the annotations shows some interesting differences in the distribution of labels between modern and historical German.