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We investigate streaming video over Differentiated Services (Diffserv) networks that can provide a number of aggregated traffic classes with increasing quality guarantee. We propose a method to measure the loss impact of a video packet on the quality of the decoded video images. We show how the optimal Quality-of-Service (QoS) mapping from the video packets into a set of traffic classes depends on the loss rates of the classes and the pricing model, and we develop an algorithm to accurately find the optimal QoS mapping. The performance of our algorithm is evaluated through computer simulations and compares favorably to an existing algorithm.