The theoretical foundation of potentiometric diffusivity and transference-number measurements is revisited, through an analysis of the diffusion-potential relaxation a concentrated binary electrolyte exhibits after being subjected to a current pulse in a planar electrolytic cell. Earlier theory is extended to include solute-volume effects, as well as being modified to incorporate a particle-fraction basis for composition and to account for the nonlinear relationship between composition differences and cell voltage. The new theory provides significant corrections when concentration polarization is very large or when electrolytes are moderately concentrated, rationalizing the unexpected voltage responses seen during some previous transport measurements. Guidelines are developed to aid the design of galvanostatic-polarization experiments involving non-aqueous electrolytes similar to those used in lithium batteries. Complete property sets are provided for 0.85 M LiPF6 in propylene carbonate and for 2.24 M LiPF6 in a mixed-carbonate solvent.