  We show a symmetry that, in the context of a composite Higgs with anarchic
flavor, can suppress the dominant CP violating contributions to $K-\bar K$
mixing. Based on previous extensions of SU(3)$_c$, we consider the case in
which the composite sector has a global SU(6) symmetry, spontaneously broken to
a subgroup containing SU(3)$\times$SU(3). We show that the interactions with
the Standard Model can spontaneously break the remaining symmetry to the
diagonal subgroup, identified with the group of color interactions, and
naturally suppress $\epsilon_K$. We consider this scenario in the context of
the Minimal Composite Higgs Model based on SO(5)/SO(4) for the electroweak
sector. By working in the framework of 2-site models, we compute the scalar
potential, determine the conditions for a successful breaking of the symmetries
and calculate the spectrum of lightest states. We find that $\epsilon_K$ can be
suppressed and the top mass reproduced for a large region of the parameter
space where the symmetries are dynamically broken. Besides other new
resonances, the model predicts the presence of a new singlet scalar state,
generally lighter than the Higgs, that could have evaded detection at
colliders.
