Doppler-free, two-photon spectroscopy has been used to investigate the transitions n2S ← 52S and n2D ← 52S of atomic rubidium, from n = 9 to 116 and n = 7 to 124, respectively, only 7.3 cm−1 from the ionization limit. Wavelengths of these transitions have been measured to an accuracy of 1 part in 107, and series formulae computed for term values and quantum defects. Hyperfine structure splittings in the 92S to 132S levels have also been measured.