  Composite Higgs models with anarchic partial compositeness require a scale of
new physics ${\cal O}(10-100)$ TeV, with the bounds being dominated by the
dipole moments and $\epsilon_K$. The presence of anarchic bilinear interactions
can change this picture. We show a solution to the SM flavor puzzle where the
electron and the Right-handed quarks of the first generation have negligible
linear interactions, and the bilinear interactions account for most of their
masses, whereas the other chiral fermions follow a similar pattern to anarchic
partial compositeness. We compute the bounds from flavor and CP violation and
show that neutron and electron dipole moments, as well as $\epsilon_K$ and
$\mu\to e\gamma$, are compatible with a new physics scale below the TeV.
$\Delta F=2$ operators involving Left-handed quarks and $\Delta F=1$ operators
with $d_L$ give the most stringent bounds in this scenario. Their Wilson
coefficients have the same origin as in anarchic partial compositeness,
requiring the masses of the new states to be larger than ${\cal O}(6-7)$ TeV.
