smallness of CKM mixing angles is due to the smallness of the off-diagonal entries with respect to the relevant diagonal entry yields the structure [@romanino], $$Y_{d}\propto \left( 
\begin{array}{ccc}
0 & \bar{\varepsilon}^{3} & {\ \bar{\varepsilon}^{3}} \\ 
. & {\bar{\varepsilon}^{2}} & {\ \bar{\varepsilon}^{2}} \\ 
. & . & 1\end{array}\right) ,~~~~~~~~~~Y_{u}\propto \left( 
\begin{array}{ccc}
0 & {\ \varepsilon ^{3}} & {\ \varepsilon ^{3}} \\ 
. & {\ \varepsilon ^{2}} & \varepsilon ^{2} \\ 
. & . & 1\end{array}\right)$$with the expansion parameters $\bar{\varepsilon}=0.15$ and $\varepsilon
=0.05 $. Some non-Abelian family symmetry models can provide such a structure quite naturally [@kingross; @spontaneous]. Here we have suppressed coefficients of ${\mathcal{O}}(1)$. This structure has $Y_{kj}<Y_{ij}$ for $i>k$ and $\ j\geq i$ and is unique if the contribution to the left-handed mixing angles from the elements below the diagonal are negligible. If one relaxes this constraint then it is possible for some of the entries to be smaller or zero (texture zeros). We will discuss both these possibilities. To do so let us first note that, although there are no direct bounds on the Yukawa couplings below the diagonal from (right-handed) mixing angles, we can obtain some upper bounds on these entries from their contributions to the mass eigenvalues. 