A subcritical reactor can be used to destroy heavy isotopes contained in the used fuel from a conventional nuclear reactor, while at the same time producing electricity. The long-lived transuranic elements in nuclear waste can in principle be fissioned, releasing energy in the process and leaving behind the fission products which are shorter-lived. This would shorten considerably the time for disposal of radioactive waste. However, some isotopes have threshold fission cross sections and therefore require a fast reactor for being fissioned. While they can be transmuted into fissile material with thermal neutrons, some nuclides need as many as three successive neutron capture reactions to reach a fissile isotope and then yet another neutron to fission. Also, they release on average too few new neutrons per fission, so that with a fuel containing a high fraction of them, criticality cannot be reached. The accelerator-driven reactor is independent of this parameter and thus can utilize these nuclides. The three most important long-term radioactive isotopes that could advantageously be handled that way are neptunium-237, americium-241 and americium-243. The nuclear weapon material plutonium-239 is also suitable although it can be expended in a cheaper way as MOX fuel or inside existing fast reactors.