The superior ability of dynamic legged locomotion in traversing rough terrain relative to wheeled or tracked mechanisms comes with the cost of fragile stability. Simple control methods that use only a few basic detection sensors and apply a single controller help robots keep their balance when traversing unforeseen rough terrain. Exploiting multiple controllers simultaneously, such as the free leg length and stiffness in our hopping monopod, can further improve robustness but is often mechanically hard to implement. This work demonstrates that a curved leg shape can improve the robustness of a robot to perturbations in both terrain levels and initial horizontal velocity without complicating the control scheme. Our work develops Spring Loaded Inverted Pendulum (SLIP) based models that manifest the coupling of the leg’s parameters and capture the rolling motion. We use these models to find an optimal combination of parameters that maximizes a measure for long-term stability – reaching a desired relative height above terrain. We demonstrate that when traversing unknown rough terrain, such optimal coupling can increase robustness to perturbations in the initial horizontal velocity by 93% relative to the optimal conventional SLIP model. We further demonstrate our results in experiments.