Isotropic hyperfine coupling constants (iHFCCs) can be easily measured by electron spin resonance spectroscopy in solution, but they have proven difficult to calculate from first principles. We test the performance of the newly developed (aug-)cc-pVXZ-t5s basis sets for hydrogen with Dunning's (aug-)cc-pVXZ and -pCVXZ basis sets for non-hydrogen atoms. Correlation is included by CCSD and CCSD(T) using UHF and ROHF references. A two-point extrapolation of cc-pVDZ:cc-pVDZ-t5s-a5 and cc-pVTZ:cc-pVTZ-t5s-a6 hydrogen iHFCCs is found to be very useful. Diffuse functions have nearly no influence on extrapolated iHFCCs. We also explore the dependence of the calculated iHFCCs on the level of theory used in optimizing the geometries. For this purpose, we optimized geometries up to the UHF-CCSD/ec-pCVQZ and UHF-CCSDT/cc-pCVTZ levels and extrapolated to the "complete basis set" limit. The calculated iHFCCs are compared to reference values, which are experimental numbers corrected for solvent and the most important vibrational effects. Our test molecules are the CH3., C2H3., and H2CN. radicals. At the highest level of theory, the largest deviations from the reference values are smaller than 3.5 G and 6%. The rms errors are below 2.1 G and 4%. The cc-pVXZ:cc-pVXZ-t5s basis set combinations perform better than the EPR-n and the Chipman [631\41] basis set. All of them are better than similarly sized basis sets that were not developed for iHFCCs. The calculated iHFCCs are influenced most strongly by the choice of basis set, the perturbative inclusion of connected triple excitations, and the choice of reference wave function and the level of theory in geometry optimization. Core correlation is necessary for the computation of iHFCCs for non-hydrogen atoms but has very little influence on the iHFCCs of hydrogen atoms. A good compromise between the cost and accuracy of hydrogen iHFCCs seems to be reached by two-point extrapolated ROHF-CCSD(T)-fc iHFCCs at UHF-MBPT(2)-fc/cc-pVTZ geometries. ROHF-MBPT(2)-fc or UHF-CCSD-fc/cc-pVTZ geometries are necessary when single excitations are not negligible.