In many problems involving Monte Carlo-type simulations, the target distribution is specified only implicitly as the invariant distribution of a Markov chain. Examples include stochastic models of nonequilibrium transport processes, queues, and chemical reactions. The lack of explicit expressions for the target distribution makes it difficult to apply standard variance reduction methods that rely on changing the dynamics, e.g. multigrid Monte Carlo. In this talk, I will describe a class of methods which can improve the accuracy of such calculations in certain situations, and illustrate the method on a simple stochastic lattice gas model, the symmetric simple exclusion process. The method is based on coupling the Markov process of interest to a second, closely-correlated process with known invariant distribution. This is joint work with Jonathan Goodman.