A self-aligning coupling is used as a vehicle to show that the Tolerance-Map (T-Map) mathematical model for geometric tolerances can distinguish between related and unrelated actual mating envelopes as described in the ASME/ISO standards. The coupling example illustrates how T-Maps (Patent No. 6963824) may be used for tolerance assignment during design of assemblies that contain non-congruent features in contact. Both worst-case and statistical measures are obtained for the variation in alignment of the axes of the two engaged parts of the coupling in terms of the tolerances. The statistical study is limited to contributions from the geometry of toleranced features and their tolerance-zones. Although contributions from characteristics of manufacturing machinery are presumed to be uniform, the method described in the paper is robust enough to include different types of manufacturing bias in the future. An important result is that any misalignment in the coupling depends only on tolerances, not on any dimension of the coupling.