The field gradients at the positive- and negative-ion nuclei in alkali halide molecules are analyzed taking account of overlaps between the atomic orbitals for the electrons within the ions and covalent binding through the transfer of electrons from the negative to positive ions. Explicit numerical calculations were performed for the case of the KCl molecule. It is shown that the inclusion of overlap effects, in addition to pure ionic contributions considered earlier, alters the field gradient in the right direction to improve the agreement with the observed field gradient at the chlorine nucleus. Charge-transfer covalency, on the other hand, increases the discrepancy with experiment. The field gradient at the positive-ion nucleus is also affected quite significantly by the inclusion of overlap effects.