Stochastic composite simulation models, such as those created via the IBM Splash prototype platform, can be used to estimate performance measures for complex stochastic systems of systems. When, as in Splash, a composite model is made up of loosely coupled component models, we propose a method for improving the efficiency of composite-model simulations. To run n Monte Carlo replications of the composite model, we execute certain component models fewer than n times, caching and re-using results as needed. The number of component-model replications is chosen to maximize an asymptotic efficiency measure that balances computation costs and estimator precision. We initiate the study of result-caching schemes by giving an exact theoretical analysis for the most basic two-model scenario, as well as outlining some approaches for obtaining the parameter values needed for result caching.