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.