Cations in 6-coordination with orbitally degenerate E-g ground states, such as Cu2+. and low-spin Co2+, play an important role in coordination chemistry-in particular, in modern complex biochemistry. The stereochemistry and the binding properties within the basic polyhedra are the subject of pronounced modifications due to vibronic coupling in such cases, but may be also significantly influenced by what is usually called an imposed strain. The latter effect makes allowance for the general observation that the host sites into which the Jahn-Teller unstable centers are substituted are seldom of O-h symmetry and built from six equal ligands. Hence, the finally observed molecular and binding structure of the pseudo-octahedral complex is the result of the combined action of vibronic coupling and strain. The closer analysis of host-site strain effects demands to distinguish between elastic strain components, which modify the force constant of the vibronically active (here, epsilon(g)) vibration, and binding strain perturbations, which take account of possibly present ligands with different binding properties. A symmetry-met semiempirical strain model on such a basis is presented and a corresponding formulation within the vibronic coupling formalism is given, on the molecular level. Well-established model examples of Cu2+ in octahedral fluoride coordination in various host solids, where a great variety of experimental results is available, are given. The derived parameters allow a detailed characterization of the structural and energy qualities of the Jahn-Teller centers, and might help to steer these properties in cases where synthesis strategies are needed. The proposed strain concept is more complex than that of Ham [F. S. Ham, Electron Paramagnetic Resonance; Plenum Press: New York, 1972; F. S. Ham, Phys. Rev. 1965, A138, 1727]; the advantage is that it is directly tied to the structure and energy of the Jahn-Teller complex in focus, although more data (experimental and possibly computed) are needed in such a model.