The conventional quantum-mechanical formulation of near-adiabatic collision theory is known to have a number of defects. These defects arise because the usual description does not account for the displacement of electronic states with moving nuclei, or for the change of momentum of the electron as it jumps from one moving nucleus to the other. The purpose of this series of papers is to develop an improved theory, in which such effects are taken into account. In this paper, we show that displacement and momentum-transfer effects can be incorporated into the theory in a very simple way, provided that the wave function is expanded in terms of electronic states that have single-center character. (Linear combinations of single-center states are also permitted.) A particular form of such an expansion is proposed, and it is shown that this expansion leads to equations in which fictitious displacement couplings are eliminated and momentum-transfer terms are included. The work of this paper and of others on this subject leads to revised notions about the definition and meaning of nonadiabatic couplings.