A power-brush apparatus has a housing, a brush rotatable on the housing about a brush axis and having bristles extending generally radially of the axis, and a drive that rotates the brush in a working direction about the axis and thereby orbits tips of the bristles about the axis. Thus when in use the brush is rotated in this working direction. A support immediately adjacent the housing carries a rigid grinding wheel having an abrasive outer surface. This wheel is biased radially against the bristle tips to sharpen and clean them while a drive relatively displaces the bristle tips and the grinding-wheel surface while the wheel is urged against the bristle tips such that the grinding wheel surface primarily engages rear sides of the bristle tips turned away from the working direction.