  The assumption of anarchic quark flavor puts serious stress on composite
Higgs models: flavor bounds imply a tuning of a few per-mille (at best) in the
Higgs potential. Composite twin Higgs (CTH) models significantly reduce this
tension by opening up a new region of parameter space, obtained by raising the
coupling among the composites close to the strong coupling limit $g_* \sim
4\pi$, thereby raising the scale of composites to around 10 TeV. This does not
lead to large tuning in the Higgs potential since the leading quantum
corrections are canceled by the twin partners (rather than the composites). We
survey the leading flavor bounds on the CTH, which correspond to tree-level
$\Delta F=2$ four-Fermi operators from Kaluza-Klein (KK) Z exchange in the kaon
system and 1-loop corrections from KK fermions to the electric dipole moment of
the neutron. We provide a parametric estimate for these bounds and also perform
a numeric scan of the parameter space using the complete calculation for both
quantities. The results confirm our expectation that CTH models accommodate
anarchic flavor significantly better than regular composite Higgs (CH) models.
Our conclusions apply both to the identical and fraternal twin cases.
