An insert (50) for a clamping element (10) having two jaws (12, 13) for clamping a rod-shaped element comprises at least one jacket element (51). Said jacket element can be inserted into one jaw (12, 13) each of the clamping element (10), thereby allowing to vary, especially reducing, the free space (11) available for a rod. The insert (50) also comprises at least one retaining section (53, 54) which fastens at least one part of the insert (50) in or on at least one of the jaws (12, 13) of the clamping element. A clamping element can be provided with two jacket elements (51), interlinked via an undulated web, or two or three juxtaposed longitudinal grooves for receiving rods having different diameters.
