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Conventional dynamic codebook reordering can often significantly enhance the achievable compression efficiency in simple one-stage vector quantization. When applied to more advanced quantizer structures, such as multi-stage vector quantizers, the performance of the technique becomes worse. This paper describes in detail an enhanced approach for dynamic codebook reordering that improves the performance by taking into account the whole quantizer structure. The significant efficiency improvements provided by the proposed approach are demonstrated in practical experiments. Though the results presented in this paper relate to a speech storage system, the proposed approach can also be employed more widely in compression applications that keep the encoder and the decoder in synchrony.