Although hand prostheses with a cosmetic covering are commercially available for disabled people, the operating effort due to the stiffness of the mechanism is high. This results in high power requirements. This paper aims to present a new concept of mechanisms for the compensation of the nonlinear stiffness of hand prostheses by using statically balanced mechanisms with a nonlinear behavior. This concept was based on a combination of stability phases of snap-through buckling in bistable spring mechanisms to create the nonlinear balancing force. To demonstrate the efficiency of the concept, an optimized design for a case study of a child-sized hand prosthesis is also presented. A pattern search method was applied for the optimization. As a result, the calculated stiffness and, thereby, the operating effort was reduced by 96%. It can be concluded from the conceptual and numerical results that the presented concept provides a highly efficient solution to the discussed problem.