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