The geometric singularity problem is one of principal difficulty when using single-gimbal control moment gyros as spacecraft attitude control devices. To overcome singularity, new steering logics are suggested in this paper which results in a reduction in the difficulty of generating gimbal rates around a singular state. One of the suggested steering laws presented is the reduced dimensional singular value decomposition steering law, which adopts the singular value decomposition in reduced dimensional forms. Two other steering laws make use of the least square method in reduced dimensional forms. All of the suggested steering laws have been generated for the compensation of the torque insufficiency. These logics are verified mathematically and simulations at a singular condition and non-singular condition are performed to see how well they work.