An investigation of relaxed alignment tolerance in monolithic ring lasers is presented. It was found that the relaxed alignment tolerance is strongly dependent on the out-of-plane angle. A preferred region for the out-of-plane angle is proposed. In this region the resonator has greatly relaxed alignment tolerances, and the unidirectional operation can be obtained under a much-lower magnetic field. Two lasers have been constructed in the region, and satisfactory performance was found, in good agreement with the theoretical analysis.