Abstract: A clamp-on stabilizer fixes the lateral position of a drill string in a borehole. The stabilizer includes a gripping sleeve with slotted and tapered ends, a stabilizer body receiving the sleeve, and a tubular locknut threaded into the body. The lower end of the stabilizer body is internally tapered to engage one tapered end of the gripping sleeve, while a ring abutting the locknut engages the other tapered end. In a preferred embodiment the tapers are different at each end of the sleeve to produce a sequential locking effect. A full-length longitudinal slot in the sleeve increases the tolerance range for objects to be clamped by the stabilizer.