  Cold, asymptotically dense three-flavor quark matter is in the color-flavor
locked (CFL) phase, in which all quarks pair in a particularly symmetric
fashion. At smaller densities, taking into account a nonzero strange quark mass
and electric and color neutrality, the CFL phase requires pairing of quarks
with mismatched Fermi momenta. We present a classification of all other
possible, less symmetric, pairing patterns and prove that none of them can
avoid this mismatch. This result suggests unconventional, e.g., spatially
inhomogeneous, superconducting phases for moderate densities.
