The hyperfine coupling constants of some small radicals containing phosphorus (PH, PH2, PF2, PCl2, PH3+, PH4, H3PF, HPF3) and for which experimental values are available are investigated using ab initio MO and DFT methods. Geometries were obtained at the UMP2, UQCISD and B3LYP levels, in combination with the 6-311G(d,p) basis set. The isotropic hyperfine coupling constants were calculated using the above methods with a variety of basis sets, in particular for the B3LYP method. For the smallest radicals (PH, PH2, PH3+ and PH4), UQCISD(T) calculations also were performed using a finite field method. Anistropic coupling constants were calculated using the PWP density functionals. The influence of geometry is discussed, pointing out that UMP2 yields geometries closer to the UQCISD than the B3LYP for this type of molecules. It is shown again that DFT, when used in conjunction with purposely tailored basis sets, is a very economic alternative to highly correlated MO methods for computing the hyperfine properties of phosphorus-containing radicals. Such a basis set, which is being introduced in this work, seems to provide a better cancellation of errors and is small enough to be used in large molecular computations while still giving reliable hyperfine coupling constants. The improved basis set is then applied to the study of three somewhat larger radicals, namely PF4, PCl4 and P2H6+.