We present initial results of a study by laser spectroscopy of the diamagnetic structure of Rydberg states of lithium designed to verify the absolute accuracy to which the energy and the magnetic field can be determined, and to confirm the results of numerical calculations of the energy level structure. Spectra are displayed in the energy regime of − 252 cm −1 to − 242 cm −1, essentially exploring the n = 21 energy manifold, at magnetic fields up to 8.6 tesla.The spectroscopic resolution, ≈ 0.001 cm −1 ,represents a major improvement over previous work.