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In circuit design with component values that are subject to variation from circuit to circuit, we often wish to find a statistical distribution for these component values that yields an acceptable level for the mean of some cost function. Statistical methods for solving this problem have become popular in recent years, especially in circuits with large numbers of varying components, as deterministic methods are hard to use in these cases. In using these methods, we are often faced with the problem of estimating the cost under one distribution given that we have sampled under another distribution. However, if the sampling distribution and the distribution under which the expected cost is to be estimated differ too much, then a poor estimator of the expected cost may be obtained. A new method of doing further sampling only in regions where the original sampling distribution under-sampled is introduced. By using this procedure, large reductions in variance are possible with only a small amount of additional sampling.