Several recent studies on the control of legged locomotion in animal and robot running focus on the influence of different leg parameters on gait stability. In a preceding investigation self-stability controls showing deadbeat behavior could be obtained by studying the dynamics of the system in dependence of the leg orientation carefully adjusted during the flight phase. Such controls allow to accommodate disturbances of the ground level without having to detect them. Here we further this method in two ways. Besides the leg orientation, we allow changes in leg stiffness during flight and show that this extension substantially improves the rejection of ground disturbances. In a human like example the tolerance of random variation in ground level over many steps increased from 3.5% to 35% of leg length. In single steps changes of about 70% leg length (either up or down) could be negotiated. The variable leg stiffness not only allows to start with flat leg orientations maximizing step tolerances but also increase the control subspace. This allows to customize self-stability controls and to consider physical and technical limitations found in animals and robots.