We present a number of experiments on parsing the Ancient Greek Dependency Treebank (AGDT), i.e. the largest syntactically annotated corpus of Ancient Greek currently available (350k words ca). Although the AGDT is rather unbalanced and far from being representative of all genres and periods of Ancient Greek, no attempt has been made so far to perform automatic dependency parsing of Ancient Greek texts. By testing and evaluating one probabilistic dependency parser (MaltParser), we focus on how to improve the parsing accuracy and how to customize a feature model that fits the distinctive properties of Ancient Greek syntax. Also, we prove the impact of genre and author diversity on parsing performances.