The sense of touch has always been challenging to replicate in robotics, but it can provide critical information when grasping objects. Nowadays, tactile sensing in artificial hands is usually limited to using external sensors which are typically costly, sensitive to disturbances, and impractical in certain applications. Alternative methods based on proprioceptive measurements exist to circumvent these issues but they are designed for fully actuated systems. Investigating this issue, the authors previously proposed a tactile sensing technique dedicated to underactuated, also known as self-adaptive, fingers based on measuring the stiffness of the mechanism as seen from the actuator. In this paper, a procedure to optimize the design of underactuated fingers in order to obtain the most accurate proprioceptive tactile data is presented. Since this tactile sensing algorithm is based on a one-to-one relationship between the contact location and the stiffness measured at the actuator, the accuracy of the former is optimized by maximizing the range of values of the latter, thereby minimizing the effect of an error on the stiffness estimation. The theoretical framework of the analysis is first presented, followed by the tactile sensing algorithm, and the optimization procedure itself. Finally, a novel design is proposed which includes a hidden proximal phalanx to overcome shortcomings in the sensing capabilities of the proposed method. This paper demonstrates that relatively simple modifications in the design of underactuated fingers allow to perform accurate tactile sensing without conventional external sensors.