A computationally efficient and highly accurate solution scheme for phase-change problems is described which combines an implicit treatment of the temperature field equations with an explicit treatment of the interface energy balance (s). This scheme avoids the iterative interaction between the field and interface solutions which characterizes a fully implicit treatment. No time-step limitations were encountered in the wide range of numerical solutions that were carried out with the methodology. The accuracy characteristics were established by comparisons with alternative solutions of a number of specific problems involving plane or radial freezing, one or two solid phases, and, in some cases, convective heating at the solid-liquid interface. Depending on the problem, the alternative solutions were analytical, semianalytical, or numerical. The accuracy level of the solid layer thicknesses given by the solution scheme were found to be in the 0.1% range.