A reduction of nuclear waste by transmutation of trans-uranium elements (TRUs), such as Pu and Minor Actinides (MAs) contained in Spent Nuclear Fuel (SNF), is a goal for future reactors. In general, countries with on-going nuclear scenarios would profit from MA mass stabilization, while transmutation of Pu and MAs from SNF could be desired in countries in nuclear phaseout. Both missions can be accomplished by employing fast reactors loaded with fuels containing different amounts of Pu and MAs in a closed (or partially closed) fuel cycle. In this paper, two 1200 MWth sodium-cooled fast reactor cores, based on the French ASTRID design, are proposed for burning TRUs (phase-out option) or only MAs (on-going option). Main attention is focused on the safety and on the transmutation performance. The coolant void effect, in the region including the core and the plenum above and the Doppler constant of both systems are negative also with irradiated fuel. The conversion ratios (CR) of the Pu and MA burners are in the ranges from 0.6 to 0.7 and from 0.5 to 0.6, respectively. These results show a large safety and transmutation potential of ASTRID type reactors.