  We show that the presence of a lightish scalar resonance, $\sigma$, that
mixes with the composite Goldstone-Higgs boson can relax the typical bounds
found in this class of models. This mechanism, inbred in models with a walking
dynamics above the condensation scale, allows for a low compositeness scale $f
\gtrsim 400$ GeV, corresponding to a misalignment angle $\sin\theta \lesssim
0.6$, contrary to the common lore of a smaller angle. According to recent
lattice results, the light $\sigma$ emerges thanks to a near-conformal phase
above the condensation scale, consistent to the requirements from flavour
physics. We study this effect in a general way, showing that it appears in all
cosets emerging from an underlying gauge-fermion dynamics, in the presence of
top partial compositeness. The scenario is testable both on the Lattice and
experimentally, as it requires the presence of a second broad Higgs-like
resonance, below 1 TeV, that can be revealed at the LHC in the $ZZ$ and
$t\bar{t}$ channels.
