Exceptionally short N-F bond distances of only 1.217 Angstrom (crystal) and 1.246 Angstrom (gas phase) have been reported for N2F+, making it the shortest N-F bond ever observed. To trace the origin of this structural phenomenon, we have analyzed the model systems N2X+, NF3X+, and NH3X+ (X = F, H) using generalized gradient approximation density functional theory at BP86/TZ2P. In good agreement with experiment, the computations yield an extremely short N-F bond for N2F+: we find N-F bond distances in N2F+, NF4+, and NH3F+ of 1.245, 1.339, and 1.375 Angstrom, respectively. The N-X bonding mechanisms are quantitatively analyzed in the framework of Kohn-Sham MO theory. At variance with the current hypothesis, reduced steric and other Pauli repulsion (of substituents or lone pairs at N with F) rather than the extent of s-p hybridization of N (i.e., sp versus sp(3)) are responsible for the much shorter N-F distance in N2F+ compared to NF4+. The results for our nitrogen compounds are furthermore discussed in the more general context of how bond lengths are determined by both bonding and repulsive orbital interactions.