Lightwave communication systems are used to transmit information at high data rates. In the process, various physical effects distort the propagating signal and can lead to errors. Systems are designed with the intent of making error probabilities extremely small, and thus overall system performance is determined by rare events. In this talk the application of importance sampling (one member of a general family of variance reduction techniques) to the numerical simulation of transmission impairments induced by amplified spontaneous emission noise in soliton-based optical transmission systems will be discussed. The method, which is based upon the soliton structure of the equations, allows numerical simulations to be concentrated on the noise realizations that are most likely to result in transmission errors, leading to speedups of several orders of magnitude over standard Monte Carlo methods. In addition, connections between this method and classical exit time problems of stochastic differential equations will be noted.