Calcium and magnesium doped beta-phase gallium oxide (β-Ga<sub>2</sub>O<sub>3</sub>) single crystals were Czochralski grown in an iridium crucible and subsequently annealed in hydrogen at ~800° C. IR spectroscopy was used to investigate the roles of Mg and Ca dopants as well as H and Ir impurities. An IR peak at 3492 cm<sup>-1</sup> was previously assigned to an O-H bondstretching mode of a MgH complex in hydrogen-annealed Ga<sub>2</sub>O<sub>3</sub>:Mg and an IR peak at 3541 cm<sup>-1</sup> is tentatively assigned to a similar mode in a CaH complex for H annealed Ga<sub>2</sub>O<sub>3</sub>:Ca. An IR peak at 5148 cm<sup>-1</sup> is attributed to the presence of Ir<sup>4+</sup> when magnesium is present. Excitation with several different wavelengths was used to confirm the position of the Ir level within the band gap. Our results suggest that isolated substitutional Ca dopants are less effective as deep acceptors than Mg. Polarization dependence of the iridium IR spectra is also discussed.