Regularization of linear prediction based mel-frequency cepstral coefficient (MFCC) extraction in speaker verification is considered. Commonly, MFCCs are extracted from the discrete Fourier transform (DFT) spectrum of speech frames. In this paper, DFT spectrum estimate is replaced with the recently proposed regularized linear prediction (RLP) method. Regularization of temporally weighted variants, weighted LP (WLP) and stabilized WLP (SWLP) which have earlier shown success in speech and speaker recognition, is also introduced. A novel type of double autocorrelation (DAC) lag windowing is also proposed to enhance robustness. Experiments on the NIST 2002 corpus indicate that regularized all-pole methods (RLP, RWLP and RSWLP) yield large improvement on recognition accuracy under additive factory and babble noise conditions in terms of both equal error rate (EER) and minimum detection cost function (MinDCF).