An improved noise suppression system (400) is disclosed which performs speech quality enhancement upon speech-plus-noise signal available at the input (205) to generate a clean speech signal at the output (265) by spectral gain modification. The noise suppression system of the present invention includes a background noise estimator (420) which generates and stores an estimate of the background noise power spectral density based upon pre-processed speech (215), as determined by the detected minima of the post-processed speech energy level. This post-processed speech (255) may be obtained directly from the output of the noise suppression system, or may be simulated by multiplying the pre-processed speech energy (225) by the channel gain values of the modification signal (245). This technique of implementing post-processed signal to generate the background noise estimate (325) provides a more accurate measurement of the background noise energy since it is based upon much cleaner speech signal. As a result, the present invention performs acoustic noise suppression in high ambient noise backgrounds with significantly less voice quality degradation.