A piston pump as a high-pressure fuel pump of a common rail system includes: a pump cylinder; a pump piston moveably mounted in a recess of the pump cylinder, the pump piston being moveable up and down in the recess; and a leakage groove arranged in the pump cylinder in a region of the recess, the leakage groove being coupled with a leakage line configured to discharge a fuel leakage. Between the pump cylinder and the pump piston a different size pairing clearance is formed in first and second portions of the pump cylinder.