In this paper we propose a method for enhancement of speech in the presence of additive noise. The objective is to selectively enhance the high SNR regions in the noisy speech in the temporal and spectral domains, without causing significant distortion in the resulting enhanced speech. This is proposed to be done at three different levels: (a) At the gross level, by identifying the regions of speech and noise in the temporal domain, (b) At the finer level, by identifying the regions of high and low SNR portions in the noisy speech, and (c) At the short-time spectrum level, by enhancing the spectral peaks over spectral valleys. Processing of noisy speech for enhancement involves mostly weighting the LP residual samples. The weighted residual samples are used to excite the time- varying LP filter to produce enhanced speech.