The effects of different basis sets and computational methods on calculated isotropic hyperfine couplings have been investigated for a set of representative small radicals (OH, H2O+, CN, HCN-, FCN-, HCCH-, CH3, CH4+, NH2, NO2, and H2CO+). Particular emphasis has been placed on the performance of the QCISD approach, when used in combination with moderately large basis sets. It is found that the 6-311+G(2df,p) basis set generally gives goad results and that the IGLO-III basis set performs nearly as well. The cc-pVXZ and aug-cc-pVXZ basis sets, on the other hand, display large and unpredictable fluctuations in hyperfine couplings even at the cc-pVQZ level. As noted previously, the reason for this erroneous behavior can be traced to the contraction of the s-shell. The error due to the unbalanced nature of the pVXZ basis sets is greatly reduced on going to the core-valence correlated aug-cc-pCVXZ sets. The calculated hyperfine coupling constants are very sensitive to changes in geometry. In turn, the geometries of radical anion systems in particular are sensitive to level of theory. The 6-311+G(2df,p) basis set has also been tested with other spin-unrestricted methods (UHF, UMP2, UQCID, and five DFT functionals), but none of these are found to perform comparably to QCISD. Inclusion of triple excitations (QCISD(T)) leads to hyperfine couplings that generally lie within 2-3 G of the QCISD results.