A screwdriver has a drive bit with a drive portion for engaging a socket within a socket-headed screw, with the drive portion being expanded by the distal end of an internal pushrod operating on the conical surface of a hold within the drive bit. The pushrod extends in a central hole within a housing. The housing may include a handle portion and a hollow shaft, with a threaded knob engaging the handle portion to move the pushrod. The drive bit may be a fixed portion of the screwdriver or an interchangeable part.