Abstract: A device for the removing of threaded fasteners with rounded off heads from nuts combinations thereof comprising a socket head having a partly cylindrical external configuration with an upper end and a lower end and an axis with a first axial length therebetween and with a surface on the upper end adapted to receive the end of a turning tool externally and internally. The lower end of the socket head is fabricated with a major recess of a generally frustroconical configuration with a second axial length. The major recess has an interior surface formed with a plurality of V-shaped projections integral with the socket and extending radially inwardly from the lower end with V-shaped valleys intermediate the V-shaped projections, thereby forming a plurality of triangles with radially interior teeth. Each of the triangles has an apex with two faces of essentially common lengths. The faces of each triangle are offset essentially equally from the radius of the cylinder.