Interfaces between two immiscible electrolytic solutions (ITIESs) provide significant contact-angle variation at substantially lower operating voltages than conventional electrowetting systems require. This voltage reduction has been justified elsewhere by a theory that rationalizes ITIES electrowetting in terms of the interfacial capacitances involved. Here, the previous theory is extended to allow more detailed descriptions of the various double-layer capacitances. Past work relied, in part, on the Gouy-Chapman theory, which incompletely describes the liquid/electrode interfaces commonly used for electrowetting. In order to assess the impact of this incompleteness, it is shown how experimental measurements of the liquid/electrode specific capacitances can be incorporated when predicting the interfacial contact-angle variation with respect to applied voltage. The extended theory refines estimates of the potential ranges over which contact angles vary, predicts more realistic response curves, and can aid the design of variable-focus lenses or display elements that exploit the low-voltage electrowetting of ITIESs.