  We investigated a general framework of the Standard Model with two Higgs
doublets (2HDSM) with suppressed flavor-changing neutral currents (FCNC's).
Loop-induced FCNC (and CP-violating) effects, when confronted with experimental
constraints for the $K$-$\bar K$, $B$-$\bar B$ and $D$-$\bar D$ mixing and for
the $(b \to s \gamma)$ decay, provide us with constraints on the values of the
dominant Yukawa couplings of the charged Higgs, i.e., the values of the
couplings of $H^{\pm}$ to $t$ and $b$ quarks. Once these {\it low} energy
experimental data relevant for the mixings and for the mentioned decay, as well
as the theoretical uncertainties for the hadronic matrix elements, are
sufficiently reduced, such analyses may be able to rule out the minimal SM and
even certain special types of the 2HDSM's (e.g., the popular ``type II'', and
``type I'' 2HDSM). In such a case, a more general 2HDSM framework discussed
here could still survive as a viable framework. Eventual detection of the
charged Higgs in high energy experiments and the measurement of its mass would
represent important information that would additonally help to rule out or to
favor the various specific 2HDSM scenarios that are contained in the discussed
2HDSM framework.
