The invention relates to an apparatus for fitting an edge profile on a narrow surface of a panel-form material in an edge-banding apparatus, having a panel carrier for accommodating a panel-form material. The panel carrier has an upper side running in a plane, having an edge-profile-feeding device, and having an edge-profile guide, said guide having at least one guide means along which or through which can be guided the edge profile. This can be fed by the edge-profile-feeding device. In order to prevent or reduce offsetting in the corner region of the panel-form material, the invention proposes that the at least one guide means should be movable relative to the panel carrier in a direction running at an angle to the plane in which the upper side of the panel carrier runs. The invention also relates to a method for fitting an edge profile, and to a furniture part produced thereby.