In many situations of digital speech communication (e.g. hands-free telephony or electronic hearing aids) the speech signal picked up by the microphone is disturbed by acoustic background noise. Therefore, adaptive filtering techniques which aim at the reduction of the disturbing noise are subject of current research activities (e.g. [1]). Although some of the already known adaptive techniques -- especially concepts with two or more microphones -- allow a significant reduction of the noise, most of the adaptive strategies result, particularly at low SNR, in a speech signal with an unnatural character due to time-variant distortions, and the occurrence of musical noise. An alternative approach, which does not affect the speech signal by time-variant distortions, is the application of a microphone array with a fixed directivity pattern aligned to the speaker's position, resulting in a suppression of spatially distributed noise sources. In this contribution it is shown that due to the proposed optimization even with only two microphones a reduction of diffuse noise sound up to 6 dB can be achieved.