We study a flat brane solution in an effective 5D action for cascading gravity in six dimensions, and propose a mechanism to screen extrinsic curvature in the presence of a large tension on the brane. The screening mechanism leaves the bulk Riemann-flat, thus making it simpler to generalize large extradimension dark energy models to higher codimensions. By studying an action with cubic interactions for the brane-bending scalar mode, we find that the perturbed action suffers from ghostlike instabilities for positive tension. The solution can be made ghost-free for sufficiently small negative tension, though the connection to 6D cascading gravity is less clear in this case.