Monte Carlo simulation can be used to estimate the bit error rate (BER) in digital lightwave communication links. However, when the link includes an avalanche photodetector (APD) receiver and is operating at a low BER, Monte Carlo simulation requires excessive execution time unless assumptions are made about the APD statistics. Techniques are presented that reduce the computational resources required to estimate the BER for these systems by two orders of magnitude. The speed-up is achieved by developing anew, more efficient random number generation algorithm for APD shot noise and by applying a tail extrapolation technique to the conditional distributions at the sample-and-decide input in the receiver. Receiver thermal noise is handled analytically. Accurate BER estimates for an NRZ direct-detection system are obtained in approximately 1.5 CPU hours on a VAXstation II using a combination of these techniques. >