In handsfree speech communication the signal to noise ratio is often poor, which makes it difficult to have a relaxed conversation. By using noise suppression, the conversation quality can be improved. This paper describes a noise suppression algorithm based on spectral subtraction. The method employs a noise and speech dependent gain function for each frequency component. Proper measures have been taken to obtain a corresponding causal filter and also to ensure that the circular convolution originating from FFT filtering yields a truly linear filtering. A novel method that uses spectrum-dependent adaptive averaging to decrease the variance of the gain function is also presented. The results show a 10-dB background noise reduction for all input SNR situations tested in the range -6 to 16 dB, as well as improvement in speech quality and reduction of noise artifacts as compared with conventional spectral subtraction methods.