The estimation of the bit error probability is fundamental to the performance evaluation of today's complex digital communication systems. Unfortunately, from a computational point of view the conventional Monte Carlo (MC) approach proves to be extremely difficult, if not impossible, for simulating such systems. As a result, it is highly desirable to devise MC methods which retain the ability to simulate complex systems, yet require substantially fewer simulation runs to estimate small probabilities. In this paper, a new quick MC technique for estimating the bit error rate (BER) of sequential decoders is presented. It is shown that the new technique is extremely efficient from a computational point of view and can be used to accurately estimate the BER for specific time invariant convolutional codes.