A method and system for improving signal-to-noise ratio of output signals of a microphone system having two or more microphones due to acoustic useful signals occurring at sides of the system, is used in hearing instruments, especially hearing aids worn on the head. High and low frequency portions (cut-off frequency between 700 Hz and 1.5 kHz, approx. 1 kHz) are processed differently. In low frequency ranges, differential microphone signals directed towards left and right are produced to determine lateral useful and noise sound levels using two directional signals. These levels are used for individual Wiener filtering for every microphone signal. The natural head shadowing effect is used in high frequency ranges as a pre-filter for noise and useful sound estimation for subsequent Wiener filtering. The methods are used in hearing instruments worn on the head individually for high or for low frequencies and in combination complement each other.