The molecular geometries and the nuclear spin-spin coupling constants of the complexes [(NC)(5)Pt-TI(CN)(n)](n-), n = 0-3, and the related system [(NC)(5)Pt-TI-Pt(CN)(5)](3-) are studied. These complexes have received considerable interest since the first charactetization of the n = 1 system by Glaser and co-workers in 1995 [J. Am. Chem. Soc. 1995, 117, 7550-7551]. For instance, these systems exhibit outstanding NMR properties, such as extremely large Pt-TI spin-spin coupling constants. For the present work, all nuclear spin-spin coupling constants J(Pt-TI), J(Pt-C), and J(TI-C) have been computed by means of a two-component relativistic density functional approach. It is demonstrated by the application of increasingly accurate computational models that both the huge JPt-TI for the complex (NC)(5)Pt-TI and the whole experimental trend among the series are entirely due to solvent effects. An approximate inclusion of the bulk solvent effects by means of a continuum model, in addition to the direct coordination, proves to be crucial. Similarly drastic effects are reported for the coupling constants between the heavy atoms and the carbon nuclei. A computational model employing the statistical average of orbital-dependent model potentials (SAOP) in addition to the solvent effects allows to accurately reproduce the experimental coupling constants within reasonable limits.