Just requiring that the determinant of the down Yukawa matrix is $\bar{\varepsilon}^{6}=1\times \frac{m_{s}}{m_{b}}\times \frac{m_{d}}{m_{b}}$ we arrive to the conclusion that $Y_{21}^{d}\leq \bar{\varepsilon}^{3}$, $Y_{31}^{d}\leq \bar{\varepsilon}$ and $Y_{32}^{d}\leq 1$, assuming no cancellation between different contributions to the determinant. With this the most general hierarchical down-quark Yukawa structure consistent with the masses and mixing angles is $$Y_d\propto \left( 
\begin{array}{ccc}
\leq \bar{\varepsilon} ^{4} & a\text{ }\bar{\varepsilon} ^{3} & {\ b}\text{ }{\bar{\varepsilon} ^{3}}
\\ 
\leq \bar{\varepsilon} ^{3} & c\text{ }{\bar{\varepsilon} ^{2}} & {\ d}\text{ }{\bar{\varepsilon} ^{2}}
\\ 
\leq \bar{\varepsilon} & \leq 1 & 1\end{array}\right).  \label{genform}$$Not all of the four coefficients $a,b,c,d$ must be ${\mathcal{O}}(1)$ allowing for the possibility of additional texture zeros. In principle the $Y_{u}$ structure could also be described by this structure with the only replacement $\bar{\varepsilon} \to \varepsilon$. As explained below, given that the SM gauge group does not relate the up and down right handed sectors, this structure with different expansion parameters in $Y^u$ and $Y^d$ emerges naturally in a multitude of flavour models both with Abelian and non-Abelian symmetries, for example in a $U(1)$ model with Frogatt-Nielsen messenger fields of different masses [@ibanez-ross]. However, our results below do not require the presence of two different expansion parameters for the up 