Binaural beamforming using signals from both left and right hearing aids offers greater potential for noise reduction than using signals from a single aid. However, wireless transmission of data imposes power constraints. Since most modern hearing aids have multiple microphones and are capable of spatial filtering, it is of interest to study the conditions when a binaural system offers significant improvements over a multi-microphone monaural system, and the situations when the noise reduction benefits are only marginal. An intelligent transmission scheme could then be designed such that signals are exchanged between the hearing aids only when the benefits are significant.