The possibility of using massive quantities of injected deuterium with and without additional admixture of lesser quantities of higher-Z impurities to effect fast thermal shutdown of a tokamak discharge without causing runaway electron avalanching is systematically studied. It is found that various combinations of deuterium alone and deuterium with impurities (helium, nitrogen, argon, and krypton) can provide acceptable runaway-free thermal shutdown. The admixture of impurities cited reduces the quantity of deuterium needed and also reduces the radiative cooling time needed for the plasma to reach final thermal equilibrium, where radiation losses balance ohmic input. In contrast, the addition of neon does not appreciably reduce deuterium quantity or promote faster cooling. This difference relative to the other impurity studies can be understood from the radiation versus plasma temperature characteristics for neon.