Bone screws with threaded screw heads that are designed to sit at or below the level of bone include features that allow them to be used to anchor sutures, either directly at the head of the screw or immediately adjacent to it. In particular, the screw head may have a hole or a pair of holes in which a bar or clip can be seated. The bar or clip carries structure that is adapted to retain a suture. Holes in the screw head can also be used to directly retain a bunching-type anchored suture, and can be threaded to retain other types of fasteners. Angled holes may be provided to allow an anchored suture to emerge adjacent to the screw head. Also disclosed are tools and methods for making holes in bone and tissue that are contiguous with the anchoring holes in the head of a surgical screw.