An advantageous method for fabricating an optical attenuator between the ends of two optical fibers uses the following steps. The axes of the cores of optical fiber ends are misaligned by an offset distance and then one of them is moved along its center axis until the ends of the fibers abut one another. Abutted ends of the optical fibers are melted. While the fiber ends are molten, surface tension aligns the axes of the cores of the optical fibers. Finally the abutted ends region of the optical fibers is cooled into a lumped optical attenuator.