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Hybrid cloud-P2P content distribution (“CloudP2P”) provides a promising alternative to the conventional cloud-based or peer-to-peer (P2P)-based large-scale content distribution. It addresses the potential limitations of these two conventional approaches while inheriting their advantages. A key strength of CloudP2P lies in the so-called bandwidth multiplier effect: by appropriately allocating a small portion of cloud (server) bandwidth Si to a peer swarm i (consisting of users interested in the same content) to seed the content, the users in the peer swarm - with an aggregate download bandwidth Di - can then distribute the content among themselves; we refer to the ratio Di/Si as the bandwidth multiplier (for peer swarm i). A major problem in the design of a CloudP2P content distribution system is therefore how to allocate cloud (server) bandwidth to peer swarms so as to maximize the overall bandwidth multiplier effect of the system. In this paper, using real-world measurements, we identify the key factors that affect the bandwidth multipliers of peer swarms and thus construct a fine-grained performance model for addressing the optimal bandwidth allocation problem (OBAP). Then we develop a fast-convergent iterative algorithm to solve OBAP. Both trace-driven simulations and prototype implementation confirm the efficacy of our solution.