  In Quantum Field Theory models of electro-weak interactions with
spontaneously broken gauge invariance, renormalizability limits to four the
degree of the Higgs potential, whose minima determine the possible vacuum
states in tree approximation. Through the discussion of some simple variants of
the Standard Model with two Higgs doublets, we show that, in some cases, the
technical limit imposed by renormalizability can prevent the observability of
some phases of the system, that would be otherwise allowed by the symmetry of
the Higgs potential. An extension of the scalar sector through suitable SU$_2$
singlet particle fields can resolve this {\em unnatural} limitation.
