A theoretical investigation of the manufacturing tolerances necessary to fabricate fused 3x3 single-mode fiber optical couplers with acceptable port-to-port uniformity in the coupling ratios is reported. Arbitrary coupler geometries are assumed, i.e. the core-to-core distances may all be the same or they may all differ. Thus, there may be one, two or three different coupling constants determining the behavior of the coupler. By using the three equations relating the fields in the three cores to one another and an approximate expression for the coupling constant, coupling ratios and uniformities can be determined for arbitrary coupler geometries. The manufacturing tolerances on core-to-core separation can be determined once the required coupling ratio and uniformity are known.