  The rotation of a black hole splits its spectrum in two, yet only one sector
is known in the highly-damped regime. We find the second, at least partly
oblate sector, with quasinormal modes approaching the total reflection
frequencies \omega(n>>1) ~ m\Omega - 2\pi iT(n-s), where \Omega and T are the
horizon angular velocity and temperature, s is the field spin, and m is an
azimuthal eigenvalue. Some physical implications are discussed.
