Method for improving noise suppression for ASR starts with a microphone receiving an audio signal including speech signal and noise signal. In each frame for frequency band of audio signal, a noise estimator detects ambient noise level and generates noise estimate value based on estimated ambient noise level, variable noise suppression target controller generates suppression target value using noise estimate value and logistic function, a gain value calculator generates a gain value based on suppression target value and noise estimate value, and combiner enhances the audio signal by the gain value to generate a clean audio signal in each frame for all frequency bands. Logistic function models desired noise suppression level that varies based on ambient noise level. Variable level of noise suppression includes low attenuation for low noise levels and progressively higher attenuation for higher noise level. Other embodiments are also described.