In a general two-Higgs-doublet model (2HDM), without the ad hoc discrete sy
mmetries to prevent tree-level flavor-changing-neutral currents, an extra p
hase angle in the charged-Higgs-fermion coupling is allowed. We show that t
he charged-Higgs amplitude interferes destructively or constructively with
the standard model amplitude for b-->s gamma depending crucially on this ph
ase angle. The popular models I and II are special cases of our analysis. A
s a result of this phase angle the severe constraint on the charged-Higgs-b
oson mass imposed by the inclusive rate of b-->s gamma from CLEO call be re
laxed. We also examine the effects of this phase angle on the neutron elect
ric dipole moment. Furthermore, we also discuss other constraints on the ch
arged-Higgs-fermion couplings coming from measurements of B-0-(B) over bar
0 mixing, rho(0), and R-b. [S0556-2821(99)02911-2].