Could the LHC two-photon signal correspond to the heavier scalar in two-Higgs-doublet models?

LHC has reported tantalizing hints for a Higgs boson of mass 125 GeV decaying into two photons. We focus on two-Higgs-doublet Models, and study the interesting possibility that the heavier scalar (H) has been seen, with the lightest scalar (h) having thus far escaped detection. Non-observation of h at LEP severely constrains the parameter-space of two-Higgs-doublet models. We analyze cases where the decay H --> h h is kinematically allowed, and cases where it is not, in the context of type I, type II, lepton-specific, and flipped models.