A injection-molded connector for single-mode optical fibers includes two mating plugs having aligned fiber-receiving holes. To keep transmission losses in the connector at an acceptable level, the eccentricity of each hole relative to its plug profile must be maintained within a fraction of a micron. The mold utilized to form the plugs includes a dual-eccentric-cam adjustment mechanism that comprises nested conically shaped cams. In a method for fabricating such plugs, rotation of the cams serves to move a part of the mold that positions a hole-forming pin. By rotating this mechanism, the eccentricity of the fiber hole relative to the profile of the molded plug can be established and maintained within the required precision.