A binaural hearing system includes a binaural pair of microphones that are configured to be located, respectively, at a first ear and a second ear of a user. The system further includes an interconnected binaural pair of sound processors that are associated with the binaural pair of microphones. The sound processors are configured to preserve an interaural level difference (“ILD”) between a first signal generated by the first microphone and a second signal generated by the second microphone. The sound processors do this by performing a contralateral gain synchronization operation to a first degree with respect to the first and second signals at the first sound processor, and to a second degree with respect to the first and second signals at the second sound processor, where the first degree is distinct from the second degree or at least one of the first and second degrees is a partial degree.