  We strengthen our previous results regarding the moduli spaces of Zoll
metrics and Zoll projective structures on S^2. In particular, we describe a
concrete, open condition which suffices to guarantee that a totally real
embedding of RP^2 in CP_2 arises from a unique Zoll projective structure on the
2-sphere. Our methods ultimately reflect the special role such structures play
in the initial value problem for the 3-dimensional Lorentzian Einstein-Weyl
equations.
