It appears that one of the most important factors limiting the usefulness of hearing aids is the high sensitivity of hearing aid users to interfering sounds. In this work, the possibility of utilizing computing power that could be packaged into a unit the size of a hearing aid in order to cancel out noises before they reach the ear was investigated. Algorithms for combining the outputs of a number of microphones so as to achieve a considerable noise reduction are proposed and evaluated, and some questions related to implementation are studied. Some experimental results based on numerical and listening tests are presented. The computation is started by indicating to the system a silent period of the main speaker. In order to minimize distortion for the main speaker, the algorithms try to produce an output that matches the first few autocorrelations of the main speaker. It is expected that the system should be able to track sufficiently slow variations in the positions of the noise sources and the main speaker.