The stable structures of odd-numbered anionic nitrogen clusters, N-2n+3(-), have been theoretically investigated in the size range n = 1-9 using a variety of quantum chemistry methods that include perturbation theory, coupled cluster, and density-functional theory with different exchange correlation functionals. We generally find that the clusters are composed of an azide chromophore N-3(-) surrounded by essentially neutral nitrogen molecules. The growth initially proceeds by placing the neutral molecules parallel to the azide anion, completing a first shell at N-13(-), above which the extra molecules arrange on the side but with a significantly lower binding energy. Comparison with the cyclic N-5(-) anionic core shows that the latter is unfavorable, the spectral signatures of both N-5(-) and N2N3- being provided in both the infrared and ultraviolet ranges. The trend of these clusters to be highly stable as (N-2)(n)N-3(-) agrees with recent mass spectrometry experiments under the cryogenic environment of helium droplets. The issues associated with the successful development of a nonreactive force field for such clusters are also highlighted.