One-nucleon removal reactions at relativistic energies have been used as spectroscopic tool to obtain information about the ground state properties of B-8 and O-23. Using the FRS at GSI, the longitudinal momentum distributions of the emerging fragments after breakup and the one-nucleon removal cross-sections were measured. The relative contributions of the remaining fragments (Be-7 and O-22) in their ground and excited states have been determined from measurements of gamma rays in coincidence with the longitudinal momentum distributions. In the B-8 case, the experimental breakup data on two different targets (C and Pb) allow a determination of the weight of the Be-7* component in the B-8 ground state wave function as (13.3+/-2.2) %. These results are discussed in the context of a theoretical three-body model. Preliminary results on O-23 indicate a spin and parity assignment of 1/2(+) in agreement with shell model predictions.