The utility of near-dissociation expansions (NDEs) for diatomic vibrational energies is tested through least-squares fitting of vibrational bandhead data for selected electronic transitions in I2, Br2, and XeCl. In these test cases, the NDEs show efficiency comparable to that for the traditional polynomials in (v+1/2). For data sets which span an intermediate range of v levels, the NDEs are clearly superior to the polynomials for extrapolating to higher v, and of comparable reliability in extrapolation to low v. However, in their approach to dissociation, the NDEs can show unphysical behavior, the correction of which requires further constraints on the form of the NDE. Also, for lengthy extrapolations the NDEs may yield optimistically precise yet erroneous values for the dissociation energy. The present best estimates of the dissociation energies (𝒟e) for the lower states involved in these calculations are 2506.0(3) cm−1 for I2(A′), 2828(8) cm−1 for Br2(A′), and 281.1(7) cm−1 for XeCl(X).