Abstract: A collet, comprising a clamping head having a front side, having interior gripping surfaces in a longitudinal zone of the clamping head for gripping a workpiece, and having an exterior surface in the form of a frustum located at least partially in the same longitudinal zone as the gripping surfaces and diverging toward the front side of the clamping head, the clamping head being divided into individual gripping jaws, at least in the longitudinal zone of the gripping surfaces, by radially- and axially-extending longitudinal slits circumferentially distributed about the clamping head. The collet includes a clamping tube separately couplable with the clamping head and having means on an end of the clamping tube facing away from the clamping head for fastening the clamping tube to an apparatus for use. Elastic members are provided in the longitudinal slits between the gripping jaws of the clamping head.