We investigate a number of cases of an impurity spin S coupled to a D-dimensional antiferromagnetic (AFM) background. The qualitative behavior of the impurity susceptibility depends upon the sublattice symmetry of the coupling, whether S is integer or half-integer, and the spectral density of the low-lying AFM excitations. When the AFM background is ordered we show that the appropriate model to consider is a non-Abelian spin-boson model. Within this model, we argue that the symmetrically coupled half-integer spin impurity retains the Curie divergence of its susceptibility for D≥2. In the case of a D=1 spin1/2 AFM chain the sublattice symmetric impurity behaves in the same way as the Kondo spin in the two-channel Kondo model and thus has a non-Curie ln(T * /T) divergent susceptibility