A self-retaining screwdriver having a plurality of diametrically opposed, radially extending blades on its tip for engagement with corresponding slots of a screw or other fastener, wherein the blades vary radially in thickness. The screwdriver also includes diametrically opposed, radially extending blades of constant thickness arranged perpendicular to the blades of radially varying thickness. Tapered blades having a thickness which increases with distance from the screwdriver axis are disclosed in one embodiment in which the blades also have a convex end surface, for use with a screw having a convex head.