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The ability of underactuated hands to grasp small objects is very limited, because the precision grasp is normally unstable. The goal of this paper is to achieve stable precision grasps by means of simple design modifications of the distal phalanges of the fingers. These modifications comprise the curving of the contact area of the distal phalanx, the application of a mechanical limit to prevent hyperextension of the distal phalanx, and the application of a compliant joint between the proximal and distal phalanges. A model is developed to calculate the limits of the finger dimensions in order to achieve stable precision grasps for different object sizes. An experimental setup is used to test the grasp stability and to verify the calculated results. It is concluded that stable precision grasps exist for the combination of concavely curved distal phalanges with a mechanical limit or with a compliant joint, if the limits to the finger dimensions are satisfied.