  For a Standard Model Higgs boson with mass between 115 GeV and 150 GeV, the
two-photon decay mode is important for discovery at the Large Hadron Collider
(LHC). We describe the interactions of a light Higgs boson in a more
model-independent fashion, and consider the parameter space where there is no
two-photon decay mode. We argue from generalities that analysis of the $t\bar t
h$ discovery mode outside its normally thought of range of applicability is
especially needed under these circumstances. We demonstrate the general
conclusion with a specific example of parameters of a type I two-Higgs doublet
theory, motivated by ideas in strongly coupled model building. We then specify
a complete set of branching fractions and discuss the implications for the LHC.
