An attachment for use with a clamp having a pair of jaws operable to clamp a workpiece therebetween, such attachment comprising a body member of such size as to be accommodated in a space between one of the jaws and the workpiece. The body member of the attachment has a first contact surface adapted to bear against a surface of the workpiece and a second, opposite contact surface adapted to bear against one of the jaws. The second contact surface is so configured as to enable the attachment body member to be substantially universally rockable relative to the jaw engaged by such attachment body member, thereby enabling the body member to occupy a position in engagement with and substantially parallel to that surface of the workpiece engaged by the attachment body member.