  We present a lattice investigation of heavy-light mesons in the quenched
approximation, using non-relativistic QCD for the heavy quark and a clover
improved Wilson formulation for the light quark. A comprehensive calculation of
the heavy-light spectrum has been performed for various heavy quark masses
around the $b$. Our results for the $B_s-B_d$ splitting agree well with the
experimental value. We find the $\Lambda_b-B$ splitting to be compatible with
experiment, albeit with large error bars. Our $B^*-B$ splitting is slightly
low, which could be explained as an effect of quenching. For the first time, we
are able to estimate the mass of $P$ states at the $B$ and compare them with
experiment.
