This research considers using center of mass (CoM) height variation as an input for balance control on a humanoid robot. Traditional balance strategies for humanoid robots are taking a step, control of the center of pressure (CoP) location, a result of the ‘ankle strategy’, and changing the angular momentum about the CoM, for example by a ‘hip strategy’. For humanoid robots, a common assumption behind these strategies is that the CoM height is predefined. However, CoM height changes can be used as an input for balance control, as for example can be observed during the landing of an athlete after a long jump. The first contributions of this work are bounds on the initial states for the variable height inverted pendulum (VHIP) from which convergence is possible to a stopped state, also known as capture regions. First, only a unilateral contact constraint is considered; negative CoM acceleration cannot be smaller than gravitational acceleration. Second, CoM height constraints are added to the model, after which a capture region can still be computed in closed-form. Third, vertical force constraints are added, after which capture regions are computed numerically using a bang-bang control law. The last capture region bridges the transition to the applied part of this work. The second contribution is a control law on vertical acceleration, suitable for application on a humanoid robot using a momentum-based control framework. Push recovery is tested on NASA’s Valkyrie humanoid robot while the robot is standing. In simulation, an increase in recoverable push of 9% can be observed when comparing to a controller that only uses CoP, when pushing the back of the robot. On hardware, an average increase of 7% can be observed for this push direction using a load sensor. Additionally, tests are conducted on hardware on Boston Dynamics’ Atlas using a medicine ball on a rope, but no improvement in recovery is observed. The control method for standing push recovery is also extended for use while the robot is walking. For Valkyrie in simulation, recovery improved the most compared with a predefined height approach for a push applied in the first part of the single support state for rear and frontal push directions. Additionally, a hardware result on Atlas while walking is briefly presented.