Level energies of g symmetry states lying just below the n = 2 dissociation threshold have been determined in a XUV + IR multi-step laser excitation experiment in HD, with an absolute accuracy of the excitation energy of 0.015 cm(-1). Intermediate B(1)Sigma(u)(+) energy levels have been calibrated by measuring transition frequencies in the U B(1)Sigma(u)(+)-X(1)Sigma(g)(+)(16, 0) Lyman band with an accuracy of 0.007 cm(-1). It is shown that v = 3 is the highest bound vibrational level in the shallow I'(1) Pi(g). outer well potential in HD, and that only two rotational levels exist. (C) 2002 Elsevier Science B.V. All rights reserved.