A binaural hearing system comprises A) left and right hearing devices, each comprising a1) an input unit providing an electric input signal representing sound; and a2) an output unit, B) a binaural level and/or gain estimator comprising b1) left and right level estimators, each comprising respective fast and slow level estimators configured to provide respective fast and slow level estimates of respective electric input signals, b2) a fast binaural level comparison unit receiving the fast level estimates of the respective left and right fast level estimators and providing a fast binaural level comparison estimate; and b3) a fast binaural level and/or gain enhancer providing respective left and right binaural level and/or gain modification estimates, in dependence of said fast binaural level comparison estimate at said left and right ears, respectively, of the user. The binaural hearing system provides that the interaural level cues are either compressed, maintained or enhanced independent of each other.