For reducing wind noise effects in a hearing instrument, a converted acoustic signal is processed in a number of frequency bands, a low frequency band of which is chosen to be a master band. A wind noise attenuation value is determined in each frequency band, based on a signal level in the frequency band concerned and on a signal level in the master band. A further wind noise reducing effect may be achieved in hearing instruments with at least two microphones where in the presence of wind noise the instrument may be switched from a directional mode to a omnidirectional mode in which an average of the output signals of the two microphones is used as signal. In single microphone hearing instruments, the microphone signal and a delayed version of this signal are used to improve wind noise detection and reduction.