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In this letter, a new discrete spectral modeling method is proposed based on a comparison of distance measure performance in an adaptive filtering context. It is shown that a new fast converging adaptive algorithm yields a more accurate estimate of the spectral envelope of the speech spectrum by minimizing COSH distance rather than the Itakura-Saito distance measure. We apply discrete spectral all-pole modeling to code-excited linear predictive coding by refining the short-term synthesis filter coefficients originally obtained by the linear prediction method. Simulation results show the enhanced harmonic and formant structure in the speech spectrum and that better speech quality is obtained.