In this paper for an object grasped by a robot hand to work in stiffness control domain we first investigate the number of fingers for successful stiffness modulation in the object operational space. Next we propose a new compliance control method for robot hands which consist of two steps. RIFDS(Resolved Inter-Finger Decoupling Solver) is to decompose the desired compliance characteristic specified in the op-erational space into the compliance characteristic in the fingertip space without inter-finger coupling and RIJDS(Resolved Inter-Joint Decoupling Solver) is to decompose the fingertip space without inter-finger coupling and RIJDS(Resolved inter-Joint Decoupling Solver) is to decompose the compliance characteristic in the finger-tip space into the compliance characteristic given in the joint space without inter-joint coupling. Based on the analysis results the finger structure should be biominetic in the sense that either kniematic redundancy or force redundancy are required to implement the proposed compliance control scheme, Five-bar fingered robot hands are used as an illustrative example 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.