The reciprocating compressor has a cylinder with a compression chamber where a piston can slide between a crank-side position and a head-side position; a piston rod is mechanically connected to the piston and during operation of the compressor, slides in a hole of the compression chamber; there is a small gap between the hole and the piston rod; in order to avoid leakage from this gap a jacket is arranged around the piston rod and is sealed on one side to the piston and on the other side to the cylinder at the gap.