One of the greatest challenges in the use of nuclear energy is the high radioactive long-lived waste which is generated during production. It must be dealt with safely and effectively. While technical solutions exist, including deep geological repositories, progress in the disposal of radioactive waste has been influenced, and in many cases delayed, by public perceptions about the safety of the technology. One of the primary reasons for this is the long life of many of radionuclides, actinides and fission products, with half-lives on the order of a hundred thousand to a million years. Problems of perceptions could be reduced significantly, according to our and many others author’s opinion, if there were a way to burn or destroy the most toxic long-lived radioactive wastes. As there are no industrial methods for waste destroying today, in this paper it was suggested a new hybrid approach: instead of final waste disposal, long-termed but yet temporal storage only, striving towards final destruction once a appropriate conditions are maintained. This new or modified old approach could affect current HLLLW management and related activities in: changes of processing technology; prolonging the time period of waste storage at temporal depositories; increasing the investment into research regarding the methods and technologies for destructions of these materials, and slowing down the investments into the very expensive final disposal repositories. It’s authors opinion that such conceptual approach would contribute the reviving interest in nuclear energy, all over the world and especially in small and developing countries.