Regulable vibration damper, in particular for a vehicle chassis, comprising a cylinder barrel which has a hydraulic fluid received therein in a sealed-off manner, comprising a piston which is axially movable within the cylinder barrel along a cylinder-barrel axis and which subdivides the cylinder barrel into two working chambers (11, 21), comprising a piston rod which is oriented parallel to the cylinder-barrel axis and which is connected to the piston, wherein the piston has at least two fluid leadthroughs (12, 22) by way of which one working chamber (11, 21) is connected to the other working chamber (21, 11), wherein a first valve assembly for damping the piston movement in a first actuation direction is arranged at a first fluid leadthrough, and wherein a second valve assembly for damping the piston movement in a second actuation direction is arranged at a second fluid leadthrough, wherein each valve assembly (13, 23) has at least one valve disc (14, 24) which, in a closed valve position, is seated on a valve seat (15, 25) and thus at least partially covers the associated fluid leadthrough (12, 22) and which, in an open valve position, is at least partially spaced apart from the valve seat (15, 25), wherein the valve seat (15, 25), the associated valve disc and the piston in each case delimit a vestibule into which the respective fluid leadthrough (12, 22) opens at an outlet side, and, in the piston, in addition to the fluid leadthroughs (12, 22), there is provided a bypass duct with throughflow cross sections of different size for the two throughflow directions (B1, B2), or there are provided multiple bypass ducts whose throughflow cross sections are, in sum total, of different size for the two throughflow directions (B1, B2), wherein, by means of the single bypass duct, a fluidic connection, or by means of the multiple bypass ducts, multiple fluidic connections, is or are formed between the two working chambers (11, 21), bypassing the vestibules, wherein openings of the bypass duct or of the bypass ducts are at least partially covered by a non-return disc which is formed separately from the valve discs (14, 24), wherein a non-return disc for limiting the throughflow cross section is arranged coaxially and axially offset with respect to a valve disc, wherein the non-return disc and the valve disc are arranged at the same side (43', 43'') of the piston, characterized in that the non-return disc, for reducing the bypass cross section, does not completely cover the inlet of the bypass duct, wherein the throughflow cross section is reduced, at least in one throughflow direction (B1, B2), by a non-return disc, wherein the non-return disc has at least one, preferably multiple radially, projecting bypass flaps, wherein the throughflow cross sections of different size for the two throughflow directions (B1, B2) are realized in that an opening of the bypass duct or openings of the bypass ducts at the two sides (43', 43'') of the piston are covered to different extents by corresponding non-return discs. wherein the valve seat (15, 25), the associated valve disc and the piston in each case delimit a vestibule into which the respective fluid leadthrough (12, 22) opens at an outlet side, and, in the piston, in addition to the fluid leadthroughs (12, 22), there is provided a bypass duct with throughflow cross sections of different size for the two throughflow directions (B1, B2), or there are provided multiple bypass ducts whose throughflow cross sections are, in sum total, of different size for the two throughflow directions (B1, B2), wherein, by means of the single bypass duct, a fluidic connection, or by means of the multiple bypass ducts, multiple fluidic connections, is or are formed between the two working chambers (11, 21), bypassing the vestibules, wherein openings of the bypass duct or of the bypass ducts are at least partially covered by a non-return disc which is formed separately from the valve discs (14, 24), wherein a non-return disc for limiting the throughflow cross section is arranged coaxially and axially offset with respect to a valve disc, wherein the non-return disc and the valve disc are arranged at the same side (43', 43'') of the piston, characterized in that the non-return disc, for reducing the bypass cross section, does not completely cover the inlet of the bypass duct, wherein the throughflow cross section is reduced, at least in one throughflow direction (B1, B2), by a non-return disc, wherein the non-return disc has at least one, preferably multiple radially, projecting bypass flaps, wherein the throughflow cross sections of different size for the two throughflow directions (B1, B2) are realized in that an opening of the bypass duct or openings of the bypass ducts at the two sides (43', 43'') of the piston are covered to different extents by corresponding non-return discs.