A magnetorheological (MR) piston includes an MR piston core, an MR piston end plate, a shim disc, and a flexible orifice disc. The end plate covers an end of the core to define a chamber and has a through passageway aligned with an MR-piston-core bypass passageway at the chamber. The shim disc and the orifice disc are positioned in the chamber. The orifice disc includes an orifice aligned with the bypass passageway at the chamber and includes an additional orifice. Under fluid pressure in a first direction the orifice disc lies substantially flat against one of the end and the MR piston end plate. Under fluid pressure in an opposite second direction the orifice disc is deflected by the presence of the shim disc to lift the additional orifice from the one of the end and the MR piston end plate.