A method of operating a hearing aid system 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 ; - 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 ; - 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. <EOS>