This paper addresses the problem of choosing the best streaming policy for distortion optimal multipath video delivery, under delay constraints. The streaming policy consists in a joint selection of the video packets to be transmitted, as well as their sending time, and the transmission path. A simple streaming model is introduced, which takes into account the video packet importance, and the dependencies among packets, and allows to compute the quality perceived by the receiver, as a function of the streaming policy. We derive an optimization problem based on the video abstraction model, under the assumption that the server knows, or can predict the state of the network. A detailed analysis of the timing constraints in multipath video streaming provides helpful insights that lead to an efficient algorithm to solve the NP-hard streaming policy optimization problem. We eventually propose a fast heuristic-based algorithm, that still provides close to optimal performance. Thanks to its limited complexity, this novel algorithm is finally demonstrated in live streaming scenarios, where it only induces a negligible distortion penalty compared to an optimal strategy. Simulation results finally show that the proposed scheduling solutions perform better than common scheduling algorithms, and represent very efficient multipath streaming strategies for both stored and live video services.