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Constant levels of perceptual quality of service is what ideally users of multimedia services expect. In most cases, however, they receive time-varying levels of quality of service. This paper describes a technique to deliver nearly constant perceptual quality of service when transmitting video sequences over differentiated services IP networks. MPEG video packets are transmitted either as low-loss premium packets or as regular best-effort packets depending on their individual perceptual importance. On a frame-by-frame basis, allocation to the premium class is performed depending on the perceptual importance of each macroblock, the desired level of quality of service and the instantaneous network state. The resulting perceptually-based, time-varying use of premium and best-effort network resources delivers nearly constant quality of service to end users and it yields significant higher PSNR values compared to constant allocation of premium bandwidth.