  Gaussian beams exist along all closed geodesics of a Zoll surface, despite
the fact that the algorithm for constructing them assumes that the closed
geodesics are non-degenerate. Similarly, there exists a global Birkhoff normal
for a Zoll Laplacian despite the degeneracy. We explain why both algorithms
work in the Zoll case and give an exact formula for the sub-principal normal
form invariant. In the case of "maximally degenerate" Zoll Laplacians, this
invariant vanishes and we obtain new geometric constraints on such Zoll
metrics.
