  Tree-level unitarity constraints on the masses of the Higgs bosons in the
general Two Higgs Doublet Model (THDM) are studied. We first consider the case
where the Higgs potential is invariant under a discrete symmetry
transformation, and derive strong constraints on the mass of the lightest
CP-even Higgs boson ($M_h$) as a function of $\tan\beta$. We then show that the
inclusion of the discrete symmetry breaking term weakens the mass bounds
considerably. It is suggested that a measurement of $M_h$ and $\tan\beta$ may
enable discrimination between the two Higgs potentials.
