In this work, we attempt to refine the methods based on autoregressive (AR) modeling for speech enhancement [1,2]. As a matter of fact, AR modelling, which is a key strategy of the methods reported in [1,2], is known to be good for representing unvoiced speech but not quite appropriate for voiced speech which is quite periodic in nature. Here, we incorporate a speech model which satisfactorily describes voiced and unvoiced speeches and silence (i.e., pauses between speech utterances) into the enhancement framework developed in [1,2], and specifically devise an algorithm for computing the optimal estimate of the clean speech in the minimum-mean-square-error sense. We also present the methods we use for estimating the model parameters and give a description of the complete enhancement procedure. Performance assessment based on spectrogram plots, objective measures and informal subjective listening tests all indicate that our method gives consistently good results.