  General results are obtained for meson mass splittings and mixings in
unquenched (coupled-channel) quark models. Theorems derived previously in
perturbation theory are generalised to the full coupled-channel system. A new
formula is obtained for the mass splittings of physical states in terms of the
splittings of the valence states. The S-wave hyperfine splitting decreases due
to unquenching, but its relation to the vector $e^+e^-$ width is unchanged;
this yields a prediction for the missing $\eta_b(3S)$. The ordinary (quenched)
quark model result that the P-wave hyperfine splitting vanishes also survives
unquenching. A ratio of mass splittings used to discriminate quarkonium
potential models is scarcely affected by unquenching.
