Developments for 3D control of the center of mass (CoM) are currently located in two local minima: on the one hand, methods that allow CoM height variations but only work in the 2D sagittal plane; on the other hand, nonconvex centroidal models that are delicate to handle. This paper presents an alternative that controls the CoM in 3D by predictive control over a convex optimization problem. The key to this development is the notion of boundedness condition, which quantifies convexly the viability of CoM trajectories.