New safety measures were proposed recently for ESFR, a design for a large European sodium-cooled fast reactor. The fissile height was reduced by 25% and 5% in the inner and outer cores, respectively; a lower fertile blanket was implemented. A unique fissile enrichment was chosen. Additional fuel subassemblies (FAs), passively operating safety rods and corium discharge tubes were introduced. In the current core, the sodium void effect is strongly reduced, that is favourable for reactor safety, but the Am and Cm balances, i.e. their mass variations under irradiation, remain positive. In the paper we investigate options for Am incineration in the core radial and lower fertile blankets by introducing there a mixture of U and Am oxides instead of U oxide and/or steel. With this mixture in the radial blanket instead of steel, the Am and total minor actinide balances approach negative and zero values, respectively. With this mixture instead of U oxide and steel in the lower blankets, these balances are negative; the sodium void effect is lower. The modified cores produce more Pu and Cm