  We establish compactness estimates for $\bar{\partial}_{M}$ on a compact
pseudoconvex CR-submanifold $M$ of $\mathbb{C}^{n}$ of hypersurface type that
satisfies the (analogue of the) geometric sufficient conditions for compactness
of the $\bar{\partial}$-Neumann operator given by the authors earlier. These
conditions are formulated in terms of certain short time flows in complex
tangential directions.
