Many network applications that require Quality-ofService QoS support, such as transmission of digital voice and video, tolerate a certain level of service degradation. In this study, a novel network service, referred to as service with bounded degradation BD service, is presented that can take advantage of the delay tolerance of applications. Di erent from previous proposals for similar services, the BD service can guarantee hard lower bounds of the service degradation. This is achieved by strictly limiting the amount of tra c that is subject to service degradation. To implement a BD service, network tra c is partitioned into components with di erent delay requirements. Policing of the trafc components is achieved by multi-level leaky buckets. A novel scheduler, referred to as EDD-BD Earliest Deadline Due - Bounded Degradation scheduler, performs switching of packets. Properties of the EDD-BD scheduler are presented and analyzed.