A general physical approach and simplified algorithm have been developed that allow utilities to choose their strategy for treatment of the most dangerous long-lived fission products (either to incinerate under neutron flux or to store in underground repository) as well as to assess the overall neutron consumption needed for their incineration in a fast neutron spectrum. It has been demonstrated that if nuclear power can solve transuranic (TRU) waste transmutation problems and be able to incinerate the most toxic long-lived nuclides, such as Tc, I, and Cs (it demands ~0.15 n/fission for all these nuclides without isotopic separation), then the long-term radiotoxicity in the underground repository will not exceed the initial radiotoxicity of uranium fuel. This is one of the most important criteria of the radiologically clean nuclear power concept. Hence, apart from TRU transmutation problems, the emphasis is now on long-lived fission product incineration.