this parameter controls simultaneously the top and bottom Yukawa, Eq. (\[yukawa\]), as well as the corrections to $Zb_L\bar b_L$. As previously discussed, to obtain the large top mass we need a sizable $\sin\theta_q$, such large $\sin\theta_q$ has at least two important consequences: ([*i*]{}) it gives a large $\delta g^{b_L}$, typically one order of magnitude larger than the desired $\delta g^{b_L}$, unless there is some symmetry protecting $Zb_L\bar b_L$ [@Agashe:2006at], ([*ii*]{}) since $\sin\theta_b$ is also large, it gives a large Yukawa for the bottom from Eq. (\[yukawa\]), leading to a large $m_b$. [^3] It is possible to invoke a symmetry to protect the $Zb_L\bar b_L$ coupling, but in this case we find that $\delta g^{b_L}$ is much smaller than the value favoured by the phenomenology. Thus, in the simplest case where each elementary field mixes with just one composite field, it is not possible to obtain simultaneously the desired spectrum for the third generation and the proper $Zb\bar b$ couplings in a natural way.

To relax this tension one can consider a more general situation, where $q^{el}_L$ mixes with two different composite multiplets $q^{1cp}$ and $q^{2cp}$, which can have different charges under SU(2)$_R^{cp}$ [@Contino:2006qr; @Bouchart:2008vp]. The elementary fields $\tilde t^{el}_R$ and 