The benefits of both a logarithmic spectral amplitude (LSA) estimation and a modeling in a generalized spectral domain (where short-time amplitudes are raised to a generalized power exponent, not restricted to magnitude or power spectrum) are combined in this contribution to achieve a better tradeoff between speech quality and noise suppression in single-channel speech enhancement. A novel gain function is derived to enhance the logarithmic generalized spectral amplitudes of noisy speech. Experiments on the CHiME-3 dataset show that it outperforms the famous minimum mean squared error (MMSE) LSA gain function of Ephraim and Malah in terms of noise suppression by 1.4 dB, while the good speech quality of the MMSE-LSA estimator is maintained.