Similarly as multimode fiber systems, practical single--mode systems require demountable connectors for terminating components, system reconfiguration, testing and maintenance. Since these single-mode systems are usually large - capacity long-haul systems, the connectors, as well as the other components, must have high performance characteristics so that the span lengths can be maximized. The first concern for the connector designer then is to minimize the insertion loss of the connectors. Since single-mode fibers have core diameters on the order of 5 to 10 microns, compared with 50 to 100 microns for multimode fibers, single-mode connector designs must provide fiber-to-fiber alignments to submicron precision. High-performance single-mode connectors, in both factory and field installed versions, have been reported that provide lateral offsets of less than 1 micron and angular misalignments of less than 0.5 degrees. For typical single-mode fibers, these alignments result in insertion losses on the order of 0.5 dB. Since reflections from connectors, and/or other components, may affect the longitudinal mode spectrum and noise characteristic of laser transmitters and cause system degradation, the return loss of the connector is also of concern to the designer. It has previously been reported that fiber-to-fiber end-face contact can substantially reduce reflections without the use of index matching, resulting in return losses of about 30 d2. Using Gaussian field theory, we will present the combined effect of lateral offsets, longitudinal offsets, and angular misalignments between two butt-jointed single-mode fibers having unequal mode-field radii. The expected insertion loss of connectors based on a statistical model of the effect of typical misalignments and fiber mismatches will be presented and compared with empirical measurements of single-mode connectors. Good agreement between the theoretical model and experimental data is realized.