Abstract: The invention is directed to a cutting tool with a cutter bit or a carving insert, which is held exchangeably in a one-piece tool support and lies in contact with opposite jaws of the tool support that form a clamping gap, with prismatic clamping surfaces disposed in common with those of the jaws and with at least one clamping element, such as a tightening screw for narrowing the clamping gap and with at least one separately formed clamping surface section, which, with respect to the direction of the clamping force initiated by the manipulated tightening screw, runs obliquely in such a manner, that a component of force, which is directed towards the open end of the clamping gap, acts upon the cutter bit.