A method of operating a hearing aid system (100, 200) of an hearing aid user comprising the steps of: - providing an input signal representing an acoustical signal from an input transducer of the hearing aid system (100, 200); - providing the input signal to an auditory nerve compressor; - selecting a minimum output level for the auditory nerve compressor, wherein the minimum output level represents a hearing threshold level of 0 dB SL of the hearing aid user; - selecting a maximum output level for the auditory nerve compressor, wherein the maximum output level represents an upper end of a range of acoustical output signal intensity levels that primarily high-spontaneous rate auditory nerve fibres respond to or represents an upper end of a range of acoustical output signal intensity levels that primarily high-spontaneous rate and medium-spontaneous rate auditory nerve fibres respond to; - defining a minimum input signal level and a maximum input signal level; - operating the auditory nerve compressor according to a compression characteristic wherein the minimum input signal level is mapped onto the minimum output level of the auditory nerve compressor, and wherein the maximum input signal level is mapped onto the maximum output level of the auditory nerve compressor; - using an output signal derived from the auditory nerve compressor output signal to drive an electrical-acoustical output transducer of the hearing aid system; and wherein the maximum output level for the auditory nerve compressor is selected from a range between: 30 and 50 dB SL in case an auditory neurodegeneration of the hearing aid user has been identified for both medium-spontaneous rate and low-spontaneous rate auditory nerve fibres or from a range between 50 and 80 dB SL in case an auditory neurodegeneration of the hearing aid user has been identified only for low-spontaneous rate auditory nerve fibres. - providing an input signal representing an acoustical signal from an input transducer of the hearing aid system (100, 200); - providing the input signal to an auditory nerve compressor; - selecting a minimum output level for the auditory nerve compressor, wherein the minimum output level represents a hearing threshold level of 0 dB SL of the hearing aid user; - selecting a maximum output level for the auditory nerve compressor, wherein the maximum output level represents an upper end of a range of acoustical output signal intensity levels that primarily high-spontaneous rate auditory nerve fibres respond to or represents an upper end of a range of acoustical output signal intensity levels that primarily high-spontaneous rate and medium-spontaneous rate auditory nerve fibres respond to; - defining a minimum input signal level and a maximum input signal level; - operating the auditory nerve compressor according to a compression characteristic wherein the minimum input signal level is mapped onto the minimum output level of the auditory nerve compressor, and wherein the maximum input signal level is mapped onto the maximum output level of the auditory nerve compressor; - using an output signal derived from the auditory nerve compressor output signal to drive an electrical-acoustical output transducer of the hearing aid system; and wherein the maximum output level for the auditory nerve compressor is selected from a range between: 30 and 50 dB SL in case an auditory neurodegeneration of the hearing aid user has been identified for both medium-spontaneous rate and low-spontaneous rate auditory nerve fibres or from a range between 50 and 80 dB SL in case an auditory neurodegeneration of the hearing aid user has been identified only for low-spontaneous rate auditory nerve fibres.