Recently, hearing aid systems where the left and right ear devices collaborate with one another have received much attention. Apart from supporting natural binaural hearing, such systems hold great potential for improving the intelligibility of speech in the presence of noise through beamforming algorithms. Binaural beamforming for hearing aids requires an exchange of microphone signals between the two devices over a wireless link. This paper studies two problems: which signal to transmit from one ear to the other, and at what bit-rate. The first problem is relevant as modern hearing aids usually contain multiple microphones, and the optimal choice for the signal to be transmitted is not obvious. The second problem is relevant as the capacity of the wireless link is limited by stringent power consumption constraints imposed by the limited battery life of hearing aids.