A piston pump for delivering fluids includes a piston, a cylinder element and a pressure chamber which is arranged between an inlet valve and an outlet valve and is closed by a cover, wherein a throttling mechanism for throttling the fluid flow is provided in the fluid flow downstream of the outlet valve, and a vehicle brake system has a piston pump of this type. The throttling mechanism includes a movable annular disc which is guided on the cylinder element and the internal diameter of which is adapted to the external diameter of the cylinder element, wherein the axial travel of the annular disc sets a variable first throttle cross section.