Incineration of 90Sr and 137Cs by thermal or fast neutrons is a very difficult problem. A 14-MeV neutron source based on inertial confinement fusion is a more appropriate choice. For the first time, the contribution of the (n,2n) reaction to incineration is revealed. The energy and nuclei balance for a system of several nuclear power plants and a fusion reactor for transmutation is analyzed. If the fusion reactor supports a sufficient number of nuclear power plants, it need not produce energy or tritium. Target and blanket material problems are considered. A laser fusion incinerator has the best prospects because of its fast neutron spectrum and high driver efficiency by target gain product.