Abstract The basal-plane ordering of oxygen vacancies into “chains,” which characterizes the tetragonal-orthorhombic structural transition in the high-temperature superconductor YBa2Cu3O7-δ, has heretofore been regarded as an example of a simple Ising lattice gas model with nearest- and next-nearest-neighbor interactions. This model is reviewed within a general framework that unifies and compares previous treatments. The observed transition temperature T 1 ≃ 1000K is, however, one to two orders of magnitude smaller than predicted by this Ising model when realistic physical values are assigned to its repulsive coupling constants. Attempts to resolve this dilemma by inclusion of farther-neighbor couplings or screening effects are shown to be unsuccessful. Rather, it appears that the crucial missing ingredients are the energy associated with Cu-O bonds, and an oxygen valence charge which depends on the atom's bonding configuration, the average valence being O- in the tetragonal phase but O2- in the orthorhom...