Isotropic and anisotropic hyperfine coupling constants of second row atoms have been studied using extended basis sets with a number of different density functionals. Local functionals give even the wrong sign for some atoms, and the same occurs when the Perdew’s correlation functional is coupled to the Becke exchange one. Much better results are obtained using the Lee-Yang-Parr correlation functional. Introduction of some Hartree-Fock exchange in the functional delivers a further significant improvement, approaching the accuracy of the most refined post-Hartree-Fock computations. Purposely tailored basis sets are also introduced which are small enough to be used in molecular computations, but still give high quality geometries and hyperfine coupling constants.