An apparatus on a flat card or roller card for textile fibres such as cotton, synthetic fibres or the like, in which a covering comprising work and cover elements lies opposite the clothing of a high-speed cylinder, in which, viewed in the direction of rotation of the cylinder, in succession there is an opening for the exit of air (exhaust airflow) and an opening for entry of air (supply airflow), past which openings a flow of fibres and air is passed, wherein, in relation to the cylinder, the spacing of the covering upstream of the exhaust air opening and the spacing of the covering downstream of the exhaust air opening are different, wherein in relation to the cylinder the spacing of the covering upstream of the exhaust opening is smaller than the spacing of the covering between exhaust air opening and supply air opening and an air flow that detaches short fibres from the flow of fibres flows along the surface of the cylinder against the direction of rotation of the cylinder and flows away with the short fibres through the exhaust air opening.