A simple model is proposed to explain the crystallographic properties of solid solutions of the alkali halides. The random system is simulated with a periodic superlattice whose energy is evaluated with the Born-Mayer model generalized to include ionic polarization. The resulting average lattice parameter and anioncation distances agree with recent EXAFS data on K1−xRbxBr, RbBr1−xIx, and KCl1−xBrx. The results show that ionic polarization plays a significant role in the determination of both interatomic distances and heats of formation.