A method operates a hearing device which performs active noise suppression for suppressing noise signals having one or more frequency components. An audiogram is provided which specifies a hearing threshold of a user of the hearing device as a function of frequency, wherein by using the audiogram it is determined which frequency components of the noise are audible to the user and which are not audible. The noise suppression is operated selectively by suppressing audible frequency components of the noise and by not suppressing inaudible frequency components of the noise. A corresponding hearing device is operated according to the method.