  Interesting contributions to $\Delta a_\mu$ from a two-Higgs-doublet-model is
coming from a two-loop Barr-Zee diagram for most part of the parameter space --
a fact that has been overlooked by some Higgs/SUSY experts. A definite positive
contribution has requirements that go against precision EW data and other known
constraints. For the case without SUSY, in particular, this is almost enough to
kill the two-Higgs-doublet-model (II). We will discuss the interplay of all the
constraints and their implications.
