  Using Heavy Quark Effective Theory with non-perturbatively determined
parameters in a quenched lattice calculation, we evaluate the splittings
between the ground state and the first two radially excited states of the $B_s$
system at static order. We also determine the splitting between first excited
and ground state, and between the $B_s^*$ and $B_s$ ground states to order
$1/m_b$. The Generalized Eigenvalue Problem and the use of all-to-all
propagators are important ingredients of our approach.
