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We present an optimally modified log-spectral amplitude estimator, which minimizes the mean-square error of the log-spectra for speech signals under signal presence uncertainty. We propose an estimator for the a priori signal-to-noise ratio (SNR), and introduce an efficient estimator for the a priori speech absence probability. Speech presence probability is estimated for each frequency bin and each frame by a soft-decision approach, which exploits the strong correlation of speech presence in neighboring frequency bins of consecutive frames. Objective and subjective evaluation confirm superiority in noise suppression and quality of the enhanced speech.