At wavelengths shorter than the actual vertical thickness of a galaxy, the bending is stabilized. The reason is that stars in a finite-thickness galaxy oscillate vertically with an unperturbed frequency κ κ z ; like any oscillator, the phase of the star's response to the imposed bending depends entirely on whether the forcing frequency k u is greater than or less than its natural frequency. If k u > κ κ z for most stars, the overall density response to the perturbation will produce a gravitational potential opposite to that imposed by the bend and the disturbance will be damped. These arguments imply that a sufficiently thick galaxy (with low κ κ z ) will be stable to bending at all wavelengths, both short and long.