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We propose a noncausal estimator for the a priori signal-to-noise ratio (SNR), and a corresponding noncausal speech enhancement algorithm. In contrast to the decision-directed estimator of Ephraim and Malah (1984), the noncausal estimator is capable of discriminating between speech onsets and noise irregularities. Onsets of speech are better preserved, while a further reduction of musical noise is achieved. Experimental results show that the noncausal estimator yields a higher improvement in the segmental SNR, lower log-spectral distortion, and better Perceptual Evaluation of Speech Quality scores (PESQ, ITU-T P.862).