Abstract: The invention concerns a collet adaptable to a machine-tool that includes a chuck for clasping a workpiece to be machined, the chuck comprising a front face, at least two clasping jaws moveably affixed to jaw position adjustment means and a control device for the said position adjustment means.The collet is comprised of a frame capable of being affixed to the chuck; a main sliding element that is slidably mounted on the frame; the collet per se affixed to the frame and fitted with several stems, the latter each comprising a frustoconical face for controlling the radial displacement of the stems, cooperating with a frustoconical face of the main sliding element; and slides slidably mounted in the frame and cooperating with the main sliding element, and capable of being joined to adjustment devices controlling the position of the holding jaw bits.One application is to provide the simple adaptation of a special collet on an existing machine-tool.