  We consider two Higgs doublet models with a softly broken U(1) symmetry, for
various limiting values of the scalar mixing angles $\alpha$ and $\beta$. These
correspond to the Standard Model Higgs particle being the lighter CP-even
scalar (alignment) or the heavier CP-even scalar (reverse alignment), and also
the limit in which some of the Yukawa couplings of this particle are of the
opposite sign from the vector boson couplings (wrong sign). In these limits we
impose a criterion for naturalness by demanding that quadratic divergences
cancel at one loop. We plot the allowed masses of the remaining physical
scalars based on naturalness, stability, perturbative unitarity and constraints
coming from the $\rho$ parameter. We also calculate the $h\to \gamma\gamma$
decay rate in the wrong sign limit.
