A fuel-injection pump, especially a direct fuel injection in spark-ignition internal-combustion engines, with at least one pump for generating a fuel flow under pressure and with a rotary slide valve moved synchronously with the drive shaft of the internal-combustion engine and intended for assigning the fuel flow to at least one injection port of the internal-combustion engine and/or for branching off the fuel flow under pump pressure into a return line, the rotary slide valve is mounted so as to be displaceable to a limited extent in the direction of its axis of rotation and/or so as to be rotatable to a limited extent in relation to the rotary drive of the rotary slide valve. Preferably, at the same time, the rotary position or displacement position of the rotary slide valve can be determined in dependence on an operating parameter of the internal-combustion engine, with the result that the axial displacement of the rotary slide valve counteracts a seizure of the rotary slide valve in its guide and determination in dependence on operating parameters affords the possibility of adjusting the injection time over a larger angular sector than would be possible in view of the geometrical limits placed on the design of the rotary slide valve.