A hearing device comprises a feedback-path estimation unit, which adaptively estimates a feedback path from an output transducer to an input transducer, and sets an adaptation-step size of an adaptive feedback-path estimation algorithm in dependence on an estimate of a background-noise spectrum. The feedback-path estimation unit provides an estimation-control signal for generating an acoustic feedback-path estimation signal having an level spectrum, which has at least one first frequency band with non-zero level and at least one second frequency band with zero level or with a non-zero level smaller than the level in the first frequency band and smaller than a background-noise level in the respective second frequency band. Background noise is detected in the second frequency band while the feedback-path estimation signal is provided. The background-noise level in the at least one first frequency band is estimated for obtaining the estimate of the background-noise spectrum. A corresponding method is described. The method is e.g. useful for estimating a feedback path during fitting of a hearing device, e.g. a hearing aid, to a particular user's needs.