Evidence for the simplification of motor control of the limbs through a reduction in the number of degrees of freedom exists in areas of research such as neuroscience, robotics, and biomechanics. Human hopping in place can be modeled well with spring-mass dynamics and provides a tractable model by which to study how the locomotor system compensates through inter-joint coordination to achieve stability of performance variables, leg length and orientation. This study provides the first evidence for how the redundancy of human leg joints may be simply coordinated to stabilize spring-mass dynamics throughout the hopping cycle using an uncontrolled manifold (UCM) analysis. We use a UCM analysis to quantify the structure of joint variance that stabilizes the hypothesized performance variables, leg length and leg orientation. For one-legged human hopping in place, we hypothesized that leg length and orientation would each be stabilized throughout the entire hopping cycle. We also hypothesized that hopping at non-preferred frequencies would be more difficult for subjects and stabilization of leg length and orientation would increase. Kinematic data from eleven subjects hopping at three frequencies (2.2, 2.8, and 3.2 Hz) were collected and analyzed within the framework of the UCM. Maximum leg length stabilization was observed at mid-stance when leg length was most susceptible to small changes in joint angles. Overall stabilization of leg length increased as subjects hopped at higher frequencies, reflecting the increased demands on the control system. The stabilization of leg orientation during aerial phase acted to position the foot at initial contact to determine velocity and trajectory of the center of mass during the stance phase. Because hopping in place does not require a change in forward velocity, the control strategy for leg orientation remained the same across frequencies. We conclude that stabilization of leg length and orientation may signify a reduction in degrees of freedom in the control system.