Abstract: A packet communications network is adapted for efficiently handling of multi-priority traffic (such as multi-media traffic) by defining an access algorithm that not only ensures the requested loss probabilities for both priorities of traffic, but also optimizes the bandwidth required to carry both priority classes. A buffer having a properly sized occupancy threshold admits high priority traffic if there is room in the buffer, but admits lower priority traffic only if the buffer occupancy is below the occupancy threshold. The resulting consolidated multi-priority traffic can then be characterized by an effective bandwidth which increases the packet network capacity substantially. The multi-priority access mechanisms require little or no changes in the prior art access mechanisms and utilize pre-existing leaky bucket, route selection and link metric mechanisms of the prior art.