A hearing system includes first and second hearing devices adapted for being located at first and second ears of a user, or for being fully or partially implanted in the head at the left and right ears of the user. The first hearing device includes a forward path having a1) an input transducer for converting a sound at the first hearing device to a first electric input signal including the sound; a processor for processing the first electric input signal, or a signal originating therefrom, and providing a first processed signal in dependence of a reduced hearing ability of the user at the first ear; an output unit adapted for providing stimuli perceivable as sound for the user at the first ear based on the first processed signal. The first hearing device further includes an analysis path having a first filter for filtering the first electric input signal and providing a first filtered signal in dependence of the reduced hearing ability of the user at the first ear; and transmitter circuitry configured to allow transmission of the first filtered signal to the second hearing device. The second hearing device includes receiver circuitry configured to allow reception of the first filtered signal from the first hearing device, and an output unit adapted for providing stimuli perceivable as sound for the user at the second ear based on the first filtered signal or a processed version thereof.