Despite the fact that histograms of speech DFT coefficients are super-Gaussian, not much attention has been paid to develop estimators under these super-Gaussian distributions in combination with perceptual meaningful distortion measures. In this paper we present log-spectral magnitude MMSE estimators under super- Gaussian densities, resulting in an estimator that is perceptually more meaningful and in line with measured histograms of speech DFT coefficients. Compared to state-of-the-art reference methods, the presented estimator leads to an improvement of the segmental SNR in the order of 0.5 dB up to 1 dB. Moreover, listening tests show that the proposed estimator leads to significant improvement for the presented estimator over state-of-the-art methods.