To investigate why the sensitivity of the Néel temperature T N of the antiferromagnetic (AF) layered copper perovskites (typically La 2CuO 4) to diamagnetic impurities such as Zn is reportedly much larger than in the AF members of the K 2NiF 4 family, we first treat the effect of a concentration c of impurities on the uncorrelated electronic states in the coherent potential approximation (CPA). Then we consider the Heisenberg hamiltonian as the large correlation limit of the Hubbard hamiltonian for a single band of impurity-modified electronic states. The correlation effects are treated variationally. The model is solved explicity by using a rectangular density of states, and we obtain the c-dependent exchange J, staggered moment S q , spin wave velocity and transverse susceptibility at zero temperature. We take into consideration several recently proposed formulae for T N in the clean limit, and include the impurity effects by exploiting the results obtained, in order to test their predictions against the experimental T N( c) data for La 2Cu 1− c Zn c O 4. Our results suggest that, to explain the difference between the K 2NiF 4 and the La 2 CuO 4 families, one should consider both the sign and the magnitude of the difference I≡ϵ B−ϵ A between impurity ( B) and host ( A) ionic potentials. The slowly decreasing trend of T N( c) in the K 2NiF 4 family is reproduced if I is negative and sizeable, or positive but very small, while the quick decrease typical of the copper perovskites requires a positive and rather large I. For reasonable values of the interaction parameters, among the several models we compare, only the model of Chakravarty, Halperin and Nelson is able to semi-quantitatively reproduce the non-linear behaviour of T N( c) reported for La 2Cu 1− c Zn c O 4, provided the spin stiffness is assumed to scale with c as appropriate to Fermi liquids.