A multi-microphone hands-free device distinguishes between non-steady noise and speech and adapts the de-noising to the presence and characteristics of the detected non-steady noise without spoiling any speech that is present. In the frequency domain, the method comprises calculating a first noise reference by analyzing spatial coherence of signals picked up, calculating a second noise reference by analyzing directions of incidence of signals picked up, estimating a main direction of incidence of signals picked up, selecting as a referent noise signal noise references as a function of estimated main direction, combining signals picked up into a noisy combined signal, calculating probability that speech is absent in the noisy combined signal on basis of respective spectral energy levels of the noisy combined signal and of the referent noise signal, and selectively reducing noise by applying variable gain that is specific to each frequency band and to each time frame.