Flexure-jointed grippers provide compliant grasping capability, have low-cost and flexible manufacturing, and are insusceptible to joint friction and wear. However, their grasp stiffness can be limited by flexure compliance such that loss-of-grasp is prone to occur for high object loads. This paper examines the application of inverted-flexure joints in a cable-driven gripper that can avoid flexure buckling and greatly enhance grasp stiffness and stability. To analyze behavior, an energy-based kinetostatic model is developed for a benchmark grasping problem and validated by hardware experiments. A multi-objective design optimization study is conducted, considering key metrics of peak flexure stress, grasp stiffness, and cable actuation force. Results show that the inverted-flexure design has significantly higher grasp stiffness (63% higher in a targeted design optimization) and requires lower actuation forces (¿20% lower in all optimization cases), compared with equivalent direct-flexure designs. An application study is conducted to validate the predicted operating performance under gravity loading of the grasped object. The results demonstrate that stable and high stiffness grasping can be achieved, even under overload conditions that lead to loss-of-grasp for conventional direct-flexure designs.