This paper proposes a systematic way to modify standard basis sets for use in NMR spin-spin coupling calculations, which allows the high sensitivity of this property to the basis set to be handled in a manner which remains computationally feasible. The new basis set series is derived by uncontracting a standard basis set, such as correlation-consistent aug-cc-pVTZ, and extending it by systematically adding tight s and d functions. For elements in different rows of the periodic table, different progressions of functions are added. The new basis sets are shown to approach the basis set limit for calculations on a range of molecules containing hydrogen and first and second row atoms.