Previous papers have described and evaluated the performance of packet discard techniques for maintaining packet integrity during overload in ATM switches but without taking into account di erent classes of service.In this paper a packet discard scheme is proposed with the goal to provide incoming ows of cells with output link bandwidth depending on the class of service they belong to. Also good performance in terms of throughput and fairness in bandwidth sharing among equal priority ows are considered as the requirements to meet.In the scenarios here considered, the proposed discard scheme is shown to provide very good results and to represent a possible solution for dealing with the most demanding data ows during congestion intervals. Numerical results are reported and discussed for di erent operating conditions and tra c patterns.