Reusable launchers and landers usually rely on throttling and thrust vector control (TVC) during the terminal phase of their descent. Since throttling is the only direct way of controlling the descent speed, it might seem indispensable for a soft precision landing. This would preclude the use of solid rocket propulsion in both classes of spacecraft and render a throttling malfunction virtually unrecoverable due to lack of controllability, unless sophisticated trajectory generation techniques were employed. In contrast, this paper demonstrates that an unthrottled lander remains fully locally controllable from both a theoretical and practical point of view. First, nonlinear controllability is shown parametrically using Lie bracket analysis. Next, a practical way to achieve this full controllability is proposed, using oscillatory TVC to modulate mean thrust while retaining independent control of the attitude and lateral axis, as demonstrated by analyzing the average dynamics. A linear state feedback controller is proposed to stabilize the resulting system, with closed-loop stability demonstrated numerically for both the average dynamics (using linearization and eigenvalues) and for the full time-dependent system (using Floquet theory). The practical performance of the control architecture is demonstrated in an example spacecraft performing a landing maneuver. The practical limitations of the oscillatory control scheme are then discussed, especially with regard to the bounds on mean thrust control authority and the practical limitations of the oscillation frequency.