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The Zipf distribution is widely used to model Web site popularity, video popularity, and file referencing behavior. In recent published work, we proposed and evaluated a Zipf-based policy for probabilistic piece selection in Peer-to-Peer (P2P) media streaming. In this current paper, we revisit this Zipf model in more detail, and identify two fundamentally different modeling approaches, namely regenerative versus degenerative Zipf models. We illustrate the differences between the two models, provide refined analytical models for each, and validate the models with simulations in the context of P2P media streaming. The results show that the regenerative model is more appropriate for P2P streaming, because of its stronger sequential progress.