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In ordinary linear prediction the speech spectral envelope is modeled by an all-pole spectrum. The error criterion employed guarantees a uniform fit across the whole frequency range. However, we know from speech perception studies that low frequencies are more important than high frequencies for perception. Therefore, a minimally redundant model would strive to achieve a uniform perceptual fit across the spectrum, which means that it should be able to represent low frequencies more accurately than high frequencies. This is achieved in the LPCW vocoder: an LPC vocoder employing our recently developed method of linear predictive warping (LPW). The result is improved speech quality for the same bit rate.