Rate allocation methods are used for variable bit rate (VBR) video transmission. The Fast rate allocation through STepest descent (FAST) is a rate allocation method that achieves valid solutions in scenarios where buffer and bandwidth may vary from client to client, respecting buffer limits and fulfilling real time processing requeriments in a JPEG2000 framework. This work restates the optimization problem and implements an expansion for FAST algorithm, allowing the adaptation to possible changes in channel bandwidth while video still transferring. The proposed method considers buffer's fullness, bandwidth changes and number of frames remainig to transfer in order to provide a valid solution. Experimental results suggest the validity of solutions whereas maintaining the initial version features.