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In this letter, the mismatch error due to the replacement of a fine with a coarse quantizer is considered, and an analytical model is proposed to describe the related distortion. Simulations show that this model is highly accurate and can be used to estimate the expected distortion of DPCM-based codecs in order to better allocating the rate. For highly correlated sources, this leads to a gain of 1 to 1.5 dB over an exhaustive search method that adopts a uniform redundancy allocation. Moreover, it permits to allocate the redundancy by an easy-to-solve analytical model of the system.