The disclosure relates to binaural hearing instruments and more particularly to reduction of processing time required in a binaural hearing aid system. According to the disclosure, there is provided a method comprising mono-directional transmission of data blocks comprising audio and/or information frames from one hearing instrument to the other hearing instrument or vice versa in a binaural hearing aid. According to the disclosure, the direction of transmission is determined by a quantity characterizing the presence of usable information content in the sound signal picked up by the hearing instruments of the binaural hearing aid. It is proposed to use one or more of local SNR, local voice activity detection indication, local level, local speech intelligibility estimate to determine the direction of transmission, although other quantities may be used.