A simulation algorithm is proposed in which the potential energy function used in a Monte Carlo simulation is replaced with one that is less expensive to evaluate, coupled with a correction step based on the difference between the two potentials. This can result in a substantial reduction in computational cost. A formal derivation of the appropriate sampling criteria is given, as well as estimates of the possible improvements in code performance. The method is demonstrated on the Lennard-Jones fluid at several state points, where speedups of as much as fourfold are achieved with negligible loss in precision. (C) 2003 American Institute of Physics.