  We study the implications of a large degree of compositeness for the light
generation quarks in composite pseudo-Nambu-Goldstone-boson Higgs models. We
focus in particular on viable scenarios where the right-handed up-type quarks
have a sizable mixing with the strong dynamics. For concreteness we assume the
latter to be characterized by an SO(5)/SO(4) symmetry with fermionic resonances
in the SO(4) singlet and fourplet representations. Singlet partners dominantly
decay to a Higgs boson and jets. As no dedicated searches are currently looking
for these final states, singlet partners can still be rather light. Conversely,
some fourplet partners dominantly decay to an electroweak gauge boson and a
jet, a signature which has been analyzed at the LHC. To constrain the parameter
space of this scenario we have reinterpreted various LHC analyses. In the limit
of first two generation degeneracy, as in minimal flavor violation or
U(2)-symmetric flavor models, fourplet partners need to be relatively heavy,
with masses above 1.8 TeV, or the level of compositeness needs to be rather
small. The situation is rather different in models that deviate from the first
two generation degeneracy paradigm, as the charm parton distribution functions
are suppressed relative to the up quark ones. The right-handed charm quark can
be composite and its partners being as light as 600 GeV, while the right-handed
up quark needs either to be mostly elementary or to have its partners as heavy
as 2 TeV. Models with fully composite singlet fermions are also analyzed,
leading to similar conclusions. Finally, we consider the case where both the
fourplet and the singlet states are present. In this case the bounds could be
significantly weaken due to a combination of smaller production rates and the
opening of new channels including cascade processes.
