A parameter-free approach to phase stability in Cu-Zn substitutional alloys is shown to describe order-disorder phenomena and structural transformations with remarkable accuracy. The method is based on a multiple-scattering description of the electronic structure properties of the random alloy. Configurational order is treated within the generalized perturbation method and the concentration-functional theory. Thermodynamical properties of α and β brasses are derived from the cluster variation method. This advanced scheme is of general validity and is expected to yield similarly accurate results for other Hume-Rothery alloys.