Abstract: An alignment sleeve (66) for holding two conically shaped portions (30--30) of plugs (24--24) each of which terminates an optical fiber (25) includes two conically shaped cavities (68, 70) communicating through a common minimal diameter plane (72). After the sleeve has been molded, a tool (100) faced with an abrasive material is inserted into each cavity of the sleeve and turned rotatably while a force is applied in a direction parallel to the longitudinal axis of the tool. This causes material to be removed from the walls defining the cavities so that when the two plugs are inserted into the cavities, the axes of the fibers will be aligned coaxially and the end faces of the fibers will have a predetermined separation. The apparatus of this invention also may be used to adjust a length measurement of plugs. This is accomplished by inserting a plug into a conically shaped cavity of a tool.