This paper considers ways to approach radiologically clean nuclear power (RCNP), i.e., an energy production technology based on a natural nuclear fuel transmutation with a simultaneous fission product transformation into stable or short-lived nuclei. Ways to limit the long-term radiotoxicity accumulation in the fuel cycle, both related to actinides and to long-lived fission products, and to limit the radiological risk related to the in-core nuclear fuel inventory are defined. Criteria and guidelines are defined in that perspective, and they are applied to the evaluation of different options such as open or closed fuel cycles, burnup extension, type of neutron spectrum, use of thorium or uranium fuel cycle, and subcriticality in the multiplying region. Meanwhile, understanding the physics implications of the requirements for an RCNP reveals that there are promising ways to improve current systems. Ideal systems, which are defined to exploit all the desirable physics features to make them better in terms of environmental impact, show potential advantages, but they are never so spectacular—and certainly are to be taken extremely carefully—in view of the need of complementary technological feasibility and cost and safety analyses, Moreover, the problem of radiation doses, which is essential for fuel cycle management and could appreciably influence the choice of the appropriate fuel cycle, have not yet been taken into account. This last aspect and more specific safety analyses, together with cost-benefit evaluations, will be the subject of future investigations.