The impact of buffer management and priority scheduling is examined in stressful scenarios when the aggregate incoming traffic is higher than the output link capacity of an Asynchronous Transfer Mode (ATM) traffic shaper. To simultaneously reduce cell loss and extreme delay behavior for two or more classes of service, we show that a dynamic priority scheme is required. We propose a scheduling algorithm where the priority of different service queues is dynamically modified to allow for the provisioning of isochronous services on one of the queues. Buffer management ensures that all service queues are guaranteed a minimum amount of memory, yet available memory can be shared between service queues when necessary. This approach guarantees that no cells are lost under strain conditions until all buffer is exhausted.