A new compressible ion model for describing the energetic components of the cohesive energy of a fully ionic crystal is developed and tested using previous ab initio results for three cubic phases of MgO. This model is physically highly transparent and improves on previous compressible ion models in two ways. First, the short-range cation-anion interaction and the rearrangement energy needed to convert a free O- ion plus a free electron into an O-2 ion having a form optimal for its in-crystal environment are decomposed into the major contributions originating from the six outermost anion electrons plus smaller terms generated by the two 2s electrons. This model transfers to the B2 and B3 phases of MgO after parametrization on the ab initio data for the B1 phase even more accurately than previous compressible ion models. Second, the separate modeling of the repulsive (permutation) and attractive (penetration) components of the short-range anion-anion interactions enables the new model to describe their subtle dependencies on the in-crystal anion environment that lie beyond the scope of previous models. The new model is also used to illuminate the behavior of two fluorite oxides. (C) 2001 American Institute of Physics.