Abstract: A fuel injection pump for a compression-ignition engine includes a cylinder having a bore therein and a pump piston which is mounted not only to reciprocate within the bore past a fuel supply port but also rotate therewithin. The pump piston has upper and lower control surfaces which each have a bowed shape. The center or centers of the control edges lies or lie above them, and in the region between the upper part loads and full load in the direction towards full load the upper control edge has a rising shape while the lower control edge has a falling shape. The lower control edge, by comparison with the remainder of its extent falls progressively less steeply towards full load and the upper control edge rises increasingly steeply, so that the compensation of delivery in accordance with speed is achieved predominantly by the upper control edge and there is obtained a speed-dependent advance of the start of delivery.