In a device for machine-making a dunnage product from a single- or multi-ply continuous paper web comprising a delivery conveyor for drawing in a paper web into the device whereby a conveying direction is defined and a cutter for separating the dunnage product from a three-dimensional strand of dunnage material formed from the paper web within the device, it is provided that a removal conveyor succeeds in the conveying direction to the cutter, the removal conveyor transporting the separated dunnage product away from the cutter.