Two-state small-polaron models commonly used to describe an electron donor—acceptor pair are reviewed. From such models, one obtains a one-dimensional model potential. In the homonuclear case, the reaction coordinate for the potential is an antisymmetric vibrational mode. Four situations are discussed in which the two-state small-polaron models break down. Frequency shifts in a nuclear mode upon addition of an electron correspond to vibronic coupling terms in the Hamiltonian which are quadratic in the nuclear coordinate. These quadratic coupling terms lead to the coupling of a totally symmetric mode. Similarly, when an additional electron state is coupled to the donor and acceptor orbitals, at least one additional (totally symmetric) mode becomes coupled to the electronic motion. If the Condon approximation is not invoked, the donor—acceptor distance coordinate becomes coupled to the electronic transition also. The same type of behaviour in the potential occurs when the electron donor—acceptor couple is subjected to an external electric field. Implications for the optical absorption line shapes and rates of electron transfer, which can be qualitatively different from the predictions of the two-state small-polaron model, are discussed.