This report addresses the problem of speech enhancement employing the Minimum Mean-Square Error (MMSE) of β-order Short Time Spectral Amplitude (STSA). We present an analytical solution for β-order MMSE estimator where Discrete Fourier Transform (DFT) coefficients of (clean) speech are modeled by Laplacian distributions. Using some approximations for the joint probability density function and the Bessel function, we also present a closed-form version of the estimator (called β-order LapMMSE). The performance of the proposed estimator is compared to the state-of-the–art spectral amplitude estimators that assume Gaussian priors for clean DFT coefficients. Comparative results demonstrate the superiority of the proposed estimator in terms of speech enhancement/ noise reduction measures.