  The masses of S- and P-wave heavy-light mesons are computed in quenched QCD
using a classically and tadpole-improved action on anisotropic lattices. Of
particular interest are the splittings among P-wave states, which have not yet
been resolved experimentally; even the ordering of these states continues to be
discussed in the literature. The present work leads to upper bounds for these
splittings, and is suggestive, but not conclusive, about the ordering.
