  Decades of precision measurements have firmly established the
Kobayashi-Maskawa phase as the dominant source of the CP violation observed in
weak quark decays. However, it is still unclear whether CP violation is
explicitly encoded in complex Yukawa matrices or instead stems from spontaneous
symmetry breaking with underlying CP-conserving Yukawa and Higgs sectors. Here
we study the latter possibility for the case of a generic two-Higgs-doublet
model. We find that theoretical constraints limit the ratio $t_\beta$ of the
vacuum expectation values to the range $0.22 \leq t_\beta \leq 4.5$ and imply
the upper bounds $M_{H^\pm}\leq 435$ GeV, $M_{H_{2}^0} \leq 485$ GeV and
$M_{H_{3}^0} \leq 545$ GeV for the charged and extra neutral Higgs masses. We
derive lower bounds on charged-Higgs couplings to bottom quarks which provide a
strong motivation to study the non-standard production and decay signatures $p
p \to qb H^\pm(\to q^\prime b)$ with all flavors $q,q^\prime=u,c,t$ in the
search for the charged Higgs boson. We further present a few benchmark
scenarios with interesting discovery potential in collider analyses.
