A computational study of the doping of alkali halide crystals (AX: A=Na and K; X=Cl and Br) by ns(2) cations (Ga+, In+, and Tl+) is presented. Active clusters of increasing size (from 33 to 177 ions) are considered in order to deal with the large scale distortions induced by the substitutional impurities. Those clusters are embedded in accurate quantum environments representing the surrounding crystalline lattice. The convergence of the distortion results with the size of the active cluster is analyzed for some selected impurity systems. The most important conclusion from this study is that distortions along the (100) and (110) crystallographic directions are not independent. Once a reliable cluster model is found, distortion trends as a function of impurity, alkali cation, and halide anion are identified and discussed. These trends may be useful when analyzing other cation impurities in similar host lattices.