Abstract: A tool support, or an extension or reduction part holding a tool support, is held by its shank in an axial bore of a socket of the tool-holding device. The socket has one or more further bores, the longitudinal axes of which each form an angle of from 0.degree. to about 5.degree. with a straight line perpendicular to the longitudinal axis of the socket. A setscrew disposed in one such further bore cooperates by means of a beveled or faceted surface at its lower end with a chucking surface running on the outside of the shank at an angle to the longitudinal axis thereof. Another setscrew may cooperate with a second such chucking surface forming an angle of about 45.degree. with the first chucking surface.