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The problem of finding the optimal set of quantized coefficients for a frame-based encoded signal is known to be of very high complexity. This paper presents an efficient method of finding the operational rate-distortion (RD) optimal set of coefficients. The major complexity reduction lies in the reformulation of the original RD-tradeoff problem, where a new set of coefficients is used as decision variables. These coefficients are connected to the orthogonalization of the set of selected frame vectors and not to the frame vectors themselves. By organizing all possible solutions as nodes in a solution tree, we use complexity saving techniques to find the optimal solution in an even more efficient way. Using an ordered vector selection process, the complexity can be again significantly reduced and efficient run-length encoding becomes feasible. Contrary to the original problem, the new problem can be solved optimally in a reasonable amount of time.