We consider a network providing Differentiated Services (DiffServ) which allow network service providers to offer different levels of Quality of Service (QoS) to different traffic streams. We focus on loss and first show that only trivial bounds could be obtained by means of traditional competitive analysis. Then we introduce a new approach for estimating loss of an online policy called lossbounded analysis. In loss-bounded analysis the loss of an online policy is bounded by the loss of an optimal offline policy plus a constant fraction of the benefit of the online policy. We relate the lossbounded analysis to the throughput-competitive analysis. We derive tight upper and lower bounds for various settings of DiffServ parameters using the new loss-bounded model. We believe that lossbounded analysis is an important technique that can complement traditional competitive analysis providing new insight and interesting results. 2002 Elsevier Science (USA). All rights reserved.