The fitting tool for screw head fasteners has a hollow space (5) inside the tool holder. The tool comprises a socket fitted into the tool holder and with a tool grip duct (6) into which the shear head of the fastener is located. After driving in the fastener additional torque is applied to shear off the head which is retained in the duct. Fitting another fastener pushes the sheared off head back into the duct and eventually into the collecting space (5). The socket can be fitted either way up and takes different sizes of fastener at each end. It is held in the tool holder by a shaped flange (9) and by a circular spring (14) gripping a groove (12) around the socket. The sheared off heads are retained by sprung grips (15).