  We consider the effect of a six-fermion interaction of the {'}t Hooft form in
the quark-quark channel on the ground state of matter at finite density. The
coupling constant for this new term is varied within the limits suggested by
naturalness. The flavor-mixing effects of the additional term destabilize the
color-flavor-locked (CFL) and, to a lesser extent, the two-color
superconducting (2SC) phases of quark matter, especially for positive values of
the coupling. For some values of the coupling, the critical density for the CFL
phase is nearly larger than the maximum density in the neutron stars. We
comment on the implications for neutron star evolution.
