The invention relates to a controllable vibration damper (1), in particular for a vehicle body, comprising a cylindrical tube (10) which has a hydraulic fluid that is sealed in the cylindrical tube, a piston (2) which is axially movable within the cylindrical tube (10) along a cylindrical tube axis (A) and which divides the cylindrical tube (10) into two work chambers (11, 21), and a piston rod (3) which is oriented parallel to the cylindrical tube axis (A) and which is connected to the piston (2) at one end, multiple fluid passages (12, 22) from one work chamber (11, 21) to the other work chamber (21, 11) being provided in the piston. A first valve assembly (13) for damping the piston movement in a first actuation direction (R1) is arranged in a first fluid passage (12), and a second valve assembly (23) for damping the piston movement in a second actuation direction (R2) is arranged in a second fluid passage (22), each valve assembly (13, 23) having at least one valve disk (14, 24) which sits on a valve seat (15, 25) in a closed valve position and is at least partly removed from the valve seat (15, 25) in an open valve position. Each valve assembly (13, 23) comprises a pilot control chamber (16, 26), and a pressure in the pilot control chamber (16, 26) urges the valve disk (14, 24) into the closed valve position, the pressure in each of the pilot control chambers (16, 26) being adjustable. According to the invention, one of the pilot control chambers (16, 26) is delimited by a base (4), a cylindrical lateral wall (5) which is stationary relative to the base (4) and which is coaxial to the cylindrical tube axis (A), and a dimensionally stable cover (6) which can be moved parallel to the cylindrical tube axis (A) in a radial manner within the cylindrical lateral wall (5).