A universal sleeve-clamp for using interchangeable jaw pieces to clamp a workpiece has a sleeve with a plurality of radially moveable elements. Features are provided for locating and attaching the jaw pieces to the radially moveable elements so that, when a clamping taper is made to bear against the radially moveable elements, the radially moveable elements, and hence the interchangeable jaw pieces, are moved radially to clamp the workpiece. The clamping taper may be externally tapered to form an expanding mandrel, or internally tapered to form a collet chuck. The jaw pieces, which are made of soft metal or other easily machinable material, may be shaped for clamping multiple diameters, clamping thin-walled workpieces or for clamping a workpiece eccentrically. A locator plate is used to give additional support to a workpiece, or to align it in a known rotational position for static fixturing.