  The positioning of a bubble inside a many fermion system does not affect the
volume, surface or curvature terms in the liquid drop expansion of the total
energy. Besides possible Coulomb effects, the only other contribution to the
ground state energy of such a system arises from shell effects. We show that
the potential energy surface is a rather shallow function of the displacement
of the bubble from the center and in most cases the preferential position of a
bubble is off center. Systems with bubbles are expected to have bands of
extremely low lying collective states, corresponding to various bubble
displacements.
