We have performed a systematic investigation of the influence of the basis set on relative spin-state energies for a number of iron compounds. In principle, with an infinitely large basis set, both Slater-type orbital (STO) and Gaussian-type orbital (GTO) series should converge to the same final answer, which is indeed what we observe for both vertical and relaxed spin-state splittings. However, we see throughout the paper that the STO basis sets give consistent and rapidly converging results, while the convergence with respect to the basis set size is much slower for the GTO basis sets. For example, the large GTO basis sets that give good results for the vertical spin-state splittings of compounds 1-3 (6-311+G**, Ahlrichs VTZ2D2P) fail for the relaxed spin-state splittings of compound 4 (where 1 is Fe-(PyPepS)(2) (PyPepSH(2) = N-(2-mercaptophenyl)-2-pyridinecarboxamide), 2 is Fe(tsalen)Cl (tsalen = N,N'-ethylenebis-(thiosalicylideneiminato)), 3 is Fe(N(CH2-o-C6H4S)(3))(1-Me-imidazole), and 4 is FeFHOH). Very demanding GTO basis sets like Dunning's correlation-consistent (cc-pVTZ, cc-pVQZ) basis sets are needed to achieve good results for these relaxed spin states. The use of popular (Pople-type) GTO, effective core potentials basis set (ECPB), or mixed ECPB(Fe):GTO(rest) basis sets is shown to lead to substantial deviations (2-10 kcal/mol, 14-24 kcal/mol for 3-21G), in particular for the high spin states that are typically placed at too low energy. Moreover, the use of an effective core potential in the ECPB basis sets results in spin-state splittings that are systematically different from the STO-GTO results.