How are we to characterise the art of Peter Greenaway, especially in the light of his new project Tulse Luper Suitcases: A Personal History of Uranium. This essay follows Lev Manovich's suggestion that he can be understood as a "database filmmaker". The database form is the key to Greenaway's work and explains why he is attracted to the possibilities of new media objects. These objects meet his demands for an anti-narrative cinema and for the film as Gesamtkunstwerk, or total work of art. The web site Tulse Luper Network offers us a model for the new project as a whole, allowing Greenaway to explore modes of interfacing and expanding the database beyond the limits of cinema. I argue that he takes up the baroque's art of exhaustion through the form of the new media object.