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We address the problem of joint path selection and source rate allocation in order to optimize the media specific quality of service in streaming of stored video sequences on multipath networks. An optimization problem is proposed in order to minimize the end-to-end distortion, which depends on video sequence dependent parameters, and network properties. An in-depth analysis of the media distortion characteristics allows us to define a low complexity algorithm for an optimal flow rate allocation in multipath network scenarios. In particular, we show that a greedy allocation of rate along paths with increasing error probability leads to an optimal solution. We argue that a network path shall not be chosen for transmission, unless all other available paths with lower error probability have been chosen. Moreover, the chosen paths should be used at their maximum available end-to-end bandwidth. Simulation results show that the optimal flow rate allocation carefully adapts the total streaming rate and the number of chosen paths, to the end-to-end transmission error probability. In many scenarios, the optimal rate allocation provides more than 20% improvement in received video quality, compared to heuristic-based algorithms. This motivates its use in multipath networks, where it optimizes media specific quality of service, and simultaneously saves network resources at the price of a very low computational complexity.