A hearing device, e.g. a hearing aid, comprises A) an input unit providing an electric input signal with a first dynamic range of levels comprising a target signal and/or a noise signal; B) an output unit providing output stimuli; C) a dynamic compressive amplification system comprising c1) a level detector unit providing a level estimate of the electric input signal; c2) a level post processing unit for providing a modified level estimate in dependence of a first control signal; c3) a level compression unit for providing a compressive amplification gain in dependence of the modified level estimate and a user's hearing data; and c4) a gain post processing unit for providing a modified compressive amplification gain in dependence of a second control signal; D) a control unit configured to provide a classification of said electric input signal, and to provide said first and second control signals based on said classification; and E) a forward gain unit for applying the modified compressive amplification gain to the electric input signal. A method of operating a hearing device is furthermore provided.