A pump unit includes a pump housing having a low-pressure inlet and a high-pressure outlet. A working medium is fed via the low-pressure inlet to a working chamber formed in the pump housing. The working medium is discharged from the working chamber via the high-pressure outlet. The pump unit also includes a pump piston channel formed in the pump housing and having a longitudinal axis. The pump unit has a first pump piston arranged movably along the longitudinal axis in the pump piston channel and coupled hydraulically to the working chamber. The pump unit also has a second pump piston arranged movably along the longitudinal axis in the pump piston channel and coupled hydraulically via a compensation volume to the first pump piston, wherein the compensation volume is coupled hydraulically to a compensation unit configured to adapt the compensation volume based on a pressure in the working chamber.