Nuclear spin-spin coupling constants (1)J(Hg-Hg) in the systems Hg-2(2+) and Hg-3(2+) represent the largest coupling constants so far observed in NMR experiments. We have performed a computational study on these ions, on Hg-2(2+) complexes with 18-crown-6 and 15-crown-5, and on Hg-3(2+) with solvent molecules and counterions. The results obtained with our recently developed program for the density functional computation of heavy nucleus spin-spin coupling constants are in good agreement with experiments. The data reveal that the bare ions Hg-2(2+) and Hg-3(2+) Would afford much larger coupling constants than those experimentally observed, with an upper limit of approximately 0.9 MHz for Hg-2(2+). This limit is much larger than that previously estimated by Huckel theory. It is demonstrated that in solution or due to complexation the experimentally determined values are much smaller than the free ion's coupling constants. With the help of intuitive MO arguments, it is illustrated how the environment strongly reduces the coupling constants in Hg-2(2+) and Hg-3(2+). The two-bond coupling constant (2)J(Hg-Hg) in Hg-3(2+) is also examined.