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Video transmission is a topic of major interest in our community. One of the most fundamental aspects behind many video transmission schemes is the bit allocation problem that occurs when variable bitrate video is transmitted under multiple rate constraints. Rate constraints are imposed by the channel capacity, buffer sizes in the server and/or client, and by the coding system. This work introduces a rate allocation method conceived from hill climbing techniques with steepest descent that requires very few computational resources. Experimental results achieved within the framework of JPEG2000 suggest that our approach commonly achieves a solution close to the global optimum.