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To obtain a reliable estimate of the a-priori signal to noise (SNR) ratio is crucial to most frequency domain speech enhancement algorithms. Recently, the low variance multitaper spectrum (MTS) estimator with wavelet denoising was suggested for the estimation of the a-priori SNR However, traditional approach directly plugs in the wavelet shrinkage denoiser and adopts the universal threshold which is not fully optimized to the characteristic of the MTS of noisy signals. In this paper, a two-stage estimation algorithm is proposed. First, the log MTS components that are dominated by noise are detected and removed in the wavelet domain. Second, a modified SUREshrink scheme is applied to further remove the noise remained in the speech spectral peaks. The new estimator is applied to the traditional Wiener filter and log MMSE speech enhancement algorithms and leads to significantly better performance.