A core-gripping device consisting of a series of three or more serrated-face, tapered wedges contained in slotted and tapered recesses cut into the inner surface of a lifter case or sleeve. The case is threaded to the inner tube of a core barrel. As the core enters the inner tube, it lifts the wedges up along the case taper. When the barrel is raised, the wedges are pulled tight, gripping the core.