Reliable calculations of hyperfine coupling constants of pi radicals, in particular, the Fermi contact term, have been found to pose a major theoretical problem. We present accurate Fermi contact couplings (FCCs) at the H and heavy atom nuclei in the CH, OH and CH3 radicals using generalized perturbation theories based on a multiconfigurational self-consistent-held (MCSCF) wave function. In addition, we analyze the spin polarization and correlation contributions to the FCC, using the CH radical as a test case. The success of our method is explained on the basis of the use of MCSCF optimized orbitals, as well as the renormalization of the coefficients of the MCSCF configurations. The scheme is more economical and of equal accuracy compared to the best results in the literature, as well as in very good agreement with experiment.