Apparatus and methodology for mechanically splicing two optical fibers of equal or different diameters. Instead of flat V-groove structure for holding the optical fibers to be spliced, embodiments of the present invention use a concave-walled channel to better align two optical fibers if they have different diameters. The cover holding the fibers in place in the concave channel is similarly curved. The improved alignment results in more area overlap between end surfaces of the two optical fibers to be spliced. This reduces insertion loss by 0.1 dB or better, at the splice junction and, therefore, improves light signal transmission. The radius of curvature of the concave structure can be approximately two to three times the radius of the optical fibers being spliced.