A bone anchor, for securing a suture to a bone, has an open proximal end and a body that tapers to a solid distal tip. The anchor is placed deep in a borehole in a bone using an insertion instrument that is inserted through the open proximal end of the anchor. The tip of the instrument is a spherical knob that snaps into a corresponding recess inside the anchor. The instrument has an oval cross-section that does not bear against the walls of the anchor during insertion. Once the anchor is in place, however, the anchor is expanded by rotating the instrument to bring the exterior of the instrument into contact with the walls of the anchor. The anchor is free to pivot about the spherical knob on the instrument, which allows the anchor to orient itself to the shape and size of the borehole.