The (1)JCC and (1)JCH spin-spin coupling constants have been calculated by means of density functional theory (DFT) for a set of derivatives of aliphatic hydrocarbons substituted with I, At, Cd, and Hg in order to evaluate the substituent and relativistic effects for these properties. The main goal was to estimate HALA (heavy-atom-on-light-atom) effects on spin-spin coupling constants and to explore the factors which may influence the HALA effect on these properties, including the nature of the heavy atom substituent and carbon hybridization. The methods applied range, in order of reduced complexity, from Dirac-Kohn-Sham method (density functional theory with four-component Dirac-Coulomb Hamiltonian), through DFT with two- and one-component Zeroth Order Regular Approximation (ZORA) Hamiltonians, to scalar non-relativistic effective core potentials with the non-relativistic Hamiltonian. Thus, we are able to compare the performance of ZORA-DFT and Dirac-Kohn-Sham methods for modelling of the HALA effects on the spin-spin coupling constants.