We present the first results on parsing the SynTagRus treebank of Russian with a data-driven dependency parser, achieving a labeled attachment score of over 82% and an unlabeled attachment score of 89%. A feature analysis shows that high parsing accuracy is crucially dependent on the use of both lexical and morphological features. We conjecture that the latter result can be generalized to richly inflected languages in general, provided that sufficient amounts of training data are available.