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We point out that, in the context of the SM, $|V^2_{13}| + | V^2_{23}|$ isexpected to be large, of order one. The fact that $|V^2_{13}| + |V^2_{23}|\approx 1.6 \times 10^{-3}$ motivates the introduction of a symmetry S whichleads to $V_{CKM} ={1\>\!\!\!\mathrm{I}} $, with only the third generation ofquarks acquiring mass. We consider two scenarios for generating the mass of thefirst two quark generations and full quark mixing. One consists of theintroduction of a second Higgs doublet which is neutral under S. The secondscenario consists of assuming New Physics at a high energy scale , contributingto the masses of light quark generations, in an effective field theoryapproach. This last scenario leads to couplings of the Higgs particle to$s\overline s$ and $c \overline c$ which are significantly enhanced withrespect to those of the SM. In both schemes, one has scalar-mediated flavour-changing neutral currents which are naturally suppressed. Flavour violating topdecays are predicted in the second scenario at the level $ \mbox{Br} (t\rightarrow h c ) \geq 5\times 10^{-5}$.

What if the Masses of the First Two Quark Families are not Generated by the Standard Higgs?