The suggested class-related rule (CRR) was tested for mixes of two and three different bursty service classes. Performance was evaluated at the ATM cell level in terms of effective assigned bandwidth with respect to the peak bandwidth allocation. The gains obtained using the CRR are significant for the various bursty classes investigated with burstiness values b>or=5. It was found that the CRR is a conservative approach, based on the extensive simulation of a wide range of cases and of the assumed traffic and multiplexing models. Performance of the CRR was then evaluated at the virtual call level in terms of call blocking probability in a group of ATM trunks with respect to the peak bandwidth allocation. It was found that the CRR gain at the virtual call level is greater than the CRR gain at the ATM cell level, thus increasing the attractiveness of using statistical bandwidth assignment. All the results reported require further careful verifications, in particular to test other types of service classes and cases of multiple streams mixed with bursty and variable-bit-rate traffic sources.>