This work addresses the transmission of pre-encoded JPEG2000 video within a video-on-demand scenario. The primary requirement for the rate allocation algorithm deployed in the server is to match the real-time processing demands of the application. Scalability in terms of complexity must be provided to supply a valid solution by a given instant of time. The FAst rate allocation through STeepest descent (FAST) method introduced in this work selects an initial (and possibly poor) solution, and iteratively improves it until time is exhausted or the algorithm finishes execution. Experimental results suggest that FAST commonly achieves solutions close to the global optimum while employing very few computational resources.