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We address the problem of distributed path selection and rate allocation for media streaming in overlay networks. Under the assumption that each node has only a local view of the network, we propose a distributed algorithm for joint path selection, and rate allocation, in order to minimize the end-to-end media distortion. The distributed algorithm performs iteratively, by greedy rate allocation for all incoming media flows on the outgoing links at each intermediate node. Our algorithm is shown to converge to the optimal rate allocation solution in a very small number of iterations, and to outperform heuristic distributed rate allocation mechanisms for a number of random network topologies.