  We determine the energies of the excited states of a heavy-light meson
$Q\bar{q}$, with a static heavy quark and light quark with mass approximately
that of the strange quark from both quenched lattices and with dynamical
fermions. We are able to explore the energies of orbital excitations up to L=3,
the spin-orbit splitting up to L=2 and the first radial excitation. These $b
\bar{s}$ mesons will be very narrow if their mass is less than 5775 MeV -- the
$BK$ threshold. We investigate this in detail and present evidence that the
scalar meson (L=1) will be very narrow and that as many as 6 $b \bar{s}$
excited states will have energies close to the $BK$ threshold and should also
be relatively narrow.
