Doppler-free two-photon spectroscopy has been used to investigate the transitions n2S ← 42S (n = 6 to 55) and n2D3/2.5/2 ← 42S (n = 5 to 50) of 39K. Wavelengths of these transitions have been measured to an accuracy of 1 part in 107, and term values, quantum defects, fine structure splittings, and isotope shifts have been evaluated. The value of the ionization limit determined from these measurements is 35 009.8232 ± 0.0010 cm−1.