Abstract: In a pump valve head for a high-pressure pump having at least three pistons, the axial support of the parts surrounding the inlet valve in the intake connection is hydrostatically enhanced. For this purpose, a fluid flow path is provided between the interior space of the intake connection adjacent the end of the side thereof which faces away from the pump cylinder space, said flow path communicating with an intermediate space between a terminal portion of the inlet valve and a closure member affixed to the intake connection, and a region downstream of the pressure valves of the pump discharge connection. This fluid flow path includes a port in a bushing surrounding the pressure valve as well as annular gaps on the outside periphery of a bushing surrounding the pressure valve, a manifold bushing surrounding a pump plunger and a bushing surrounding the inlet valve.