High-pressure pump for delivering fuel, for example diesel or gasoline, comprising - a housing, - at least one piston for delivering fuel, - at least one cylinder for the mounting of the at least one piston, - a recess which is formed in the housing and which serves for the arrangement of an overflow valve, - an overflow valve which is arranged within the recess and which has an inlet opening and at least one outlet opening, wherein the recess has a first, inner end and a second, outer end, the overflow valve comprising - a valve housing with a valve cylinder, - a closing piston which is movable within the valve cylinder between a closed position and an open position, such that in the closed position, the valve is closed, and in the open position, the valve is open, - an inlet opening for the feed of a fluid within a cylinder chamber enclosed by the valve cylinder, - at least one outlet opening for the discharge of the fluid that has been introduced into the cylinder chamber, - an elastic valve element, in particular valve spring, which is connected to the closing piston and by means of which a pressure force can be exerted on the closing piston, which pressure force is oriented oppositely to a pressure force that can be imparted on the closing piston by the fluid within the cylinder chamber, such that the closing piston is movable between the closed position and the open position by means of the pressure force exerted on the closing piston by the elastic valve element and by the fluid, wherein - the valve housing has, on the outer side, no fixing device for axial fastening in the recess on the housing of the high-pressure pump, characterized in that the high-pressure pump comprises a drive shaft with at least one cam and comprises a lubrication chamber, wherein the at least one piston is supported indirectly on the drive shaft by means of the at least one cam, such that the at least one piston can perform a translational movement on the basis of a rotational movement of the drive shaft, and the second, outer end of the recess serves for conducting fuel through the lubrication chamber, and the cylinder chamber is divided by the closing piston into a first cylinder chamber part and a second cylinder chamber part, and the inlet opening and the at least one outlet opening open into the first cylinder chamber part, and the elastic valve element is arranged within the second cylinder chamber part as spring chamber, and a compensation opening opens into the second cylinder chamber part through the valve housing. - a housing, - at least one piston for delivering fuel, - at least one cylinder for the mounting of the at least one piston, - a recess which is formed in the housing and which serves for the arrangement of an overflow valve, - an overflow valve which is arranged within the recess and which has an inlet opening and at least one outlet opening, wherein the recess has a first, inner end and a second, outer end, the overflow valve comprising - a valve housing with a valve cylinder, - a closing piston which is movable within the valve cylinder between a closed position and an open position, such that in the closed position, the valve is closed, and in the open position, the valve is open, - an inlet opening for the feed of a fluid within a cylinder chamber enclosed by the valve cylinder, - at least one outlet opening for the discharge of the fluid that has been introduced into the cylinder chamber, - an elastic valve element, in particular valve spring, which is connected to the closing piston and by means of which a pressure force can be exerted on the closing piston, which pressure force is oriented oppositely to a pressure force that can be imparted on the closing piston by the fluid within the cylinder chamber, such that the closing piston is movable between the closed position and the open position by means of the pressure force exerted on the closing piston by the elastic valve element and by the fluid, wherein - the valve housing has, on the outer side, no fixing device for axial fastening in the recess on the housing of the high-pressure pump,