In digital communication systems the probability of a bit error is usually on the order of 10-6 or so.To simulate an event in order to find its probability, you need to "hit" that event several times in order to get a good estimate of it.Typically then, for rare events, one might need to generate 108 to 109 independent random variables.This imposes severe if not impossible constraints on the random number generators commonly available.We are studying methodologies whereby the probabilistic systems under consideration are "twisted" into new ones where the events under study are much more likely to occur.One then "retwists" the estimates obtained here to derive the desired estimate for the original system.Orders of magnitude of better performance can be obtained from these twisted simulations.