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In this paper, a modified two-step compliance control method for robot hands is proposed: resolved interfinger decoupling solver (RIFDS) and resolved interjoint decoupling solver (RIJDS). For this, we first investigate how many fingers are necessary to successfully implement stiffness characteristics in the operational space. RIFDS is then proposed to decompose the desired compliance characteristic specified in the operational space into the compliance characteristic in the fingertip space without interfinger coupling, and RIJDS is also proposed to decompose the compliance characteristic in the fingertip space without interjoint coupling. It is found in the process of RIFDS that some nondiagonal stiffness elements specified in the operational space cannot be planned arbitrarily, due to grasping geometry. Similar to independent finger control, RIJDS aims at independent joint control. This scheme facilitates the joint servo control. To show the effectiveness of the proposed compliance control method, some experimental results are illustrated for a compliant task by using two- and three-fingered hands, which consist of five-bar finger mechanisms. It is concluded that grasping geometry and finger structure are crucial to successfully performing multifingered hands operations.