Underactuated compliant robotic hands exploit passive mechanics and joint coupling to reduce the number of actuators required to achieve grasp robustness in unstructured environments. Reduced actuation requirements generally serve to decrease design cost and improve grasp planning efficiency, but overzealous simplification of an actuation topology, coupled with insufficient tuning of mechanical compliance and hand kinematics, can adversely affect grasp quality and adaptability. This paper presents a computational framework for reducing the mechanical complexity of robotic hand actuation topologies without significantly decreasing grasp robustness. Open-source grasp planning software and well-established grasp quality metrics are used to simulate a fully-actuated, 24 DOF anthropomorphic robotic hand grasping a set of daily living objects. DOFs are systematically demoted or removed from the hand actuation topology according to their contribution to grasp quality. The resulting actuation topology contained 22% fewer DOFs, 51% less aggregate joint motion, and required 82% less grasp planning time than the fully-actuated design, but decreased average grasp quality by only 11%.