This paper shows the extent to which treebanks of Ancient Greek play a central role in the ongoing Pedalion project at the University of Leuven. Building on diverse treebanks readily available today, the project aims to make progress in the automated parsing of classical and postclassical Greek texts. Rather than developing new technology as such, our project endeavours to make deliberate and methodical use of the technology that already exists, essentially by combining and adapting both technology and data. This contribution offers a 'roadmap' of our project, surveying (a) the existing work on which we can rely, (b) the strategies which we adopt to reach better results in the automated processing of Ancient Greek and (c) the deliverables that have already been realised or are forthcoming.