  A remarkably simple regularity in the energies of 0+ states in a broad class
of collective models is discussed. A single formula for all 0+ states in
flat-bottomed infinite potentials that depends only on the number of dimensions
and a simpler expression applicable to all three IBA symmetries in the large
boson number limit are presented. Finally, a connection between the energy
expression for 0+ states given by the X(5) model and the predictions of the IBA
near the critical point is explored.
