Transforming syntactic representations in order to improve parsing accuracy has been exploited successfully in statistical parsing systems using constituency-based representations. In this paper, we show that similar transformations can give substantial improvements also in data-driven dependency parsing. Experiments on the Prague Dependency Treebank show that systematic transformations of coordinate structures and verb groups result in a 10% error reduction for a deterministic data-driven dependency parser. Combining these transformations with previously proposed techniques for recovering non-projective dependencies leads to state-of-the-art accuracy for the given data set.