  We present new variants of the Two Higgs-Doublet Model where all Yukawa
couplings with physical Higgs bosons are controlled by the quark mixing
matrices of both chiralities, as well as, in one case, the ratio between the
two scalar doublets' vacuum expectation values. We obtain these by imposing
approximate symmetries on the Lagrangian which, in one of the cases, clearly
reveals the model to be the electroweak remnant of the Minimal Left-Right
Symmetric Model. We also argue for the benefits of the bidoublet notation in
the Two Higgs-Doublet Model context for uncovering new models.
