It is shown that the oxygen-ordered superstructures observed experimentally in YBa₂Cu₃O_z can be understood in terms of an Ising Hamiltonian containing screened Coulomb repulsions between any two oxygen sites, augmented with a short-range attractive covalent interaction between oxygen sites adjoined by a copper atom. Spatially modulated commensurate phases separated by smooth soliton-like domain walls are obtained through Monte Carlo simulations. These simulations indicate the existence of a complete devil's staircase of phases. It is predicted that the plateau fine structure of the T_c-z curve and the bond valence sum also exhibit experimentally observable staircase behaviour.