  We consider the Two-Higgs-Doublet Model and determine the range of parameters
for which CP violation and Flavor Changing Neutral Current effects are
naturally small. It corresponds to small values of the mass parameter m_{12}^2,
describing soft (\phi_1,\phi_2) mixing in the potential. We discuss how, in
this approach, some Higgs bosons can be heavy, with mass of the order of 1 TeV.
  The possibility that at the Tevatron, LHC and an e^+e^- Linear Collider, only
one Higgs boson will be found, with properties indistinguishable from those in
the Standard Model (SM), we define as the SM-like scenario. While this scenario
can be obtained with large \mu^2 \sim \Re m_{12}^2 parameter, in which case
there is decoupling, we here discuss the opposite case of small \mu^2, without
decoupling.
