Local density functional calculations on a series of small, neutral radicals demonstrate that the unrestricted Kohn-Sham wavefunction is much less contaminated by higher spin states than its unrestricted Hartree-Fock counterpart, even for radicals which exhibit major contamination in their standard UHF wavefunction. A study of the dissociation curves for the OH and CN radicals shows that the UKS wavefunction remains essentially spin pure out to about 1.5 rimes the equilibrium bond length. Some general observations regarding spin contamination in unrestricted SCF wavefunctions are presented.