This is the second of a series of articles reporting critically evaluated rotational-vibrational line positions, transition intensities, pressure dependences, and energy levels, with associated critically reviewed assignments and uncertainties, for all the main isotopologues of water. This article presents energy levels and line positions of the following singly deuterated isotopologues of water: HD16O, HD17O, and HD18O. The MARVEL (measured active rotational-vibrational energy levels) procedure is used to determine the levels, the lines, and their self-consistent uncertainties for the spectral regions 0-22708, 0-1674, and 0-12105cm-1 for HD16O, HD17O, and HD18O, respectively. For HD16O, 54740 transitions were analyzed from 76 sources, the lines come from spectra recorded both at room temperature and from hot samples. These lines correspond to 36690 distinct assignments and 8818 energy levels. For HD17O, only 485 transitions could be analyzed from three sources; the lines correspond to 162 MARVEL energy levels. For HD18O, 8729 transitions were analyzed from 11 sources and these lines correspond to 1864 energy levels. The energy levels are checked against ones determined from accurate variational nuclear motion computations employing exact kinetic energy operators. This comparison shows that the measured transitions account for about 86% of the anticipated absorbance of HD16O at 296K and that the transitions predicted by the MARVEL energy levels account for essentially all the remaining absorbance. The extensive list of MARVEL lines and levels obtained are given in the Supplementary Material of this article, as well as in a distributed information system applied to water, W@DIS, where they can easily be retrieved. In addition, the transition and energy level information for H2 17O and H2 18O, given in the first paper of this series [Tennyson, et al. J Quant Spectr Rad Transfer 2009;110:573-96], has been updated.