Simulation is used to investigate and compare the impact of two different traffic shaping policies on the quality of connectionless services in two ATM network topologies with various levels of traffic load. The first topology is asymmetric and bicentric, and is a possible candidate for an Italian ATM network. The second topology is symmetric and monocentric, and is a possible candidate for a Hungarian ATM network. The performance parameters collected during the execution of simulation runs comprise cell and message loss probabilities, cell and message delay jitter distributions, and the number of cells brought to destination that must be discarded because some other cells of the same message were lost.