Energy levels of the complexes formed by Ga vacancies binding one or more deuterium (or hydrogen) atoms are investigated by low-temperature photoluminescence. Since the as-grown, nondeuterated material is unintentionally doped p type, the emission is possible because of ‘‘internal’’ recombination from a D donor in an adjacent bond-center position and the ground levels of the different possible vacancy configurations, with zero, one, or more D atoms trapped in its dangling bonds. At 2 K, the transitions occur at 1.14, 1.19–1.22, 1.33–1.30, and 1.34 eV, and the last two have never been observed before. The given energy ranges correspond to laser excitation increasing from the lowest to highest level, for a given D treatment of the material. We explain the new transitions and the multiplet character of some of the bands in terms of the possible different ways of accommodating the D atoms inside the vacancy. The level separation in our data is less than that predicted theoretically for the ‘‘bare’’ vacancy with a fully unrelaxed lattice.