For an object grasped by a robot hand to work in the compliance control domain, we first analyze a necessary condition for successful stiffness modulation in the operational space. Next, we propose a compliance control method for robot hands which consist of two steps: the RIFDS (resolved inter-finger decoupling solver) decomposes the desired compliance characteristic specified in the operational space into the compliance characteristic in the fingertip space without inter-finger coupling; and the RIJDS (resolved inter-joint decoupling solver) decomposes the compliance characteristic in the fingertip space into the compliance characteristic in the joint space without inter-joint coupling. According to the analysis results, the finger structure should be biomimetic in the sense that either kinematic redundancy or force redundancy are required to implement the proposed compliance control scheme. Five-bar fingered robot hands are treated as illustrative examples to implement the proposed compliance control method. To show the effectiveness of the proposed compliance control method, simulations are performed for two-fingered and three-fingered robot hands.