Importance sampling (IS) is the most widely used efficiency improvement method for rare-event simulation. When estimating the probability of a rare event, the IS estimator is the product of an indicator function (that the rare event has occurred) by a likelihood ratio. Reducing the variance of that likelihood ratio can increase the efficiency of the IS estimator if (a) this does not reduce significantly the probability of the rare event under IS, and (b) this does not require much more work. In

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... this paper, we explain how this can be achieved via weight windows and illustrate the idea by numerical examples. The savings can be large in some situations. We also show how the technique can backlash when the weight windows are wrongly selected.