M/G/1 queues, where G is a heavy-tailed distribution, have applications in Internet modeling and modeling for insurance claim risk. The Pareto distribution is a special heavy-tailed distribution called a power-tailed distribution, and has been found to serve as adequate models for many of these situations. However, to get the waiting time distribution, one must resort to numerical methods, e.g., simulation. Many difficulties arise in simulating queues with Pareto service and we investigate why this may be so. Even if we are willing to consider truncated Pareto service, there still can be problems in simulating if the truncation point (maximum service time possible) is too large.