The pump unit (10) comprises a pump housing (15) having a low-pressure inlet (17) and a high-pressure outlet (19). A working medium is fed via the low-pressure inlet (17) to a working chamber (20) which is formed in the pump housing (15). The working medium is discharged from the working chamber (20) via the high-pressure outlet (19). Furthermore, the pump unit (10) comprises a pump piston channel (36) which is formed in the pump housing (15) and has a longitudinal axis (L1). The pump unit (10) has a first pump piston (32) which is arranged movably along the longitudinal axis (L1) in the pump piston channel (36) and is coupled hydraulically to the working chamber (20). Furthermore, the pump unit (10) has a second pump piston (32) which is arranged movably along the longitudinal axis (L1) in the pump piston channel (36) and is coupled hydraulically via a compensation volume (100) to the first pump piston (32), wherein the compensation volume (100) is coupled hydraulically to a compensation unit (110) which is configured to adapt the compensation volume (100) in a manner which is dependent on a pressure in the working chamber (20).
