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Monte Carlo simulations are, in a sense, overly detailed when the objective of an analysis is to evaluate the steady state distribution of an underlying stochastic process. This paper describes an alternative simulation methodology [shaped simulation] that provides improved speed and accuracy, but limits the level of detail that can be extracted from the output of the simulation. The rationale for shaped simulation is presented for both discrete and continuous time Markov processes, as well as semi-Markov processes that can be analyzed using embedded Markov chains.