This paper introduces a novel speech enhancement system based on a wavelet denoising framework. In this system, the noisy speech is first preprocessed using a generalized spectral subtraction method to initially lower the noise level with negligible speech distortion. A perceptual wavelet transform is then used to decompose the resulting speech signal into critical bands. Threshold estimation is implemented that is both time and frequency dependent, providing robustness to non-stationary and correlated noisy environments. Finally, to eliminate the "musical noise" artifact, we apply a modified Ephraim/Malah suppression rule to the thresholding operation - adaptive denoising. Both objective and subjective experiments prove that the new speech enhancement system is capable of significant noise reduction with little speech distortion.