We investigate three alternatives for combining a deterministic approximation with a stochastic simulation estimator: (1) binary choice, (2) linear combination, and (3) Bayesian analysis. Making a binary choice, based on compatibility of the simulation estimator with the approximation, provides at best a 20% improvement in simulation efficiency. More effective is taking a linear combination of the approximation and the simulation estimator using weights estimated from the simulation data, which provides at best a 50% improvement in simulation efficiency. The Bayesian analysis yields a linear combination with weights that are a function of the simulation data and the prior distribution on the approximation error; the efficiency depends upon the quality of the prior distribution. © 1997 Published by Elsevier Science B.V.