mixings $0.6\lesssim \sin\theta_b\lesssim1$ and $0.35\lesssim \sin\theta_{q2}\lesssim 0.65$ to achieve the right corrections for the couplings. The bottom mass imposes as a constraint that the larger the mixings the smaller the composite Yukawa couplings $y_{cp}^b$, thus in this case we obtain $0.1\lesssim y_{cp}^b\lesssim 0.5$, introducing some tuning in the composite sector. Note that $y_{cp}^b\ll g_{cp},y_{cp}^t$, since the top mass gives us a lower bound $y_{cp}^t\gtrsim 2$ and we are considering $g_{cp}\sim 3$. A similar effect is observed if we fix $\tan\theta_A=1/8$ but increase $M$. As an example, for $M=3.4$ TeV the same range of mixings and Yukawas as in the previous case are needed to obtain the right couplings and spectrum, introducing again some tuning in the composite sector. Another possibility is to decrease $\tan\theta_A$ and $M$ simultaneously, in this case there is a partial compensation between the effects of a smaller elementary/composite mixing in the gauge sector and a lower composite scale. However for smaller $M$ we obtain larger corrections to other EW precision observables, like the $S$ and $T$ parameter, as well as flavour observables, that prefer a larger $M$.

We have also investigated embedding $[T1]$ for the $t_R$ partner in the composite sector. This case is very similar 