While state-of-the-art approaches obtain an estimate of the a priori SNR by adaptively smoothing its maximum likelihood estimate in the frequency domain, we selectively smooth the maximum likelihood estimate in the cepstral domain. In the cepstral domain the noisy speech signal is decomposed into coefficients related mainly to the speech envelope, the excitation, and noise. As in the cepstral domain coefficients that represent speech can be robustly determined, we can apply little smoothing to speech coefficients and strong smoothing to noise coefficients. Thus, speech components are preserved and musical noise is suppressed. In speech enhancement experiments we obtain consistent improvements over the well known decision-directed approach.