A well-known problem with linear prediction is that its estimate of the spectral envelope often has sharp peaks for high-pitch speakers. These peaks are anomalies resulting from contamination of the spectral envelope by the spectral fine structure. We investigate the method of regularized linear prediction to find a better estimate of the spectral envelope and compare the method to the commonly used approach of bandwidth expansion. We present simulations over voiced frames of female speakers from the TIMIT database, where the envelope modeling accuracy is measured using a log spectral distortion measure. We also investigate the coding properties of the methods. The results indicate that the new regularized LP method is superior to bandwidth expansion, with an insignificant increase in computational complexity.