In the European Sodium Fast Reactor (ESFR) project supported by EURATOM in 2008-2012, a concept for a large 3600 MWth sodium-cooled fast reactor design was investigated. In particular, reference core designs with oxide and carbide fuel were optimized to improve their safety parameters. Uncertainties in these parameters were evaluated for the oxide option. Core modifications were performed first to reduce the sodium void reactivity effect. Introduction of a large sodium plenum with an absorber layer above the core and a lower axial fertile blanket improve the total sodium void effect appreciably, bringing it close to zero for a core with fresh fuel, in line with results obtained worldwide, while not influencing substantially other core physics parameters. Therefore an optimized configuration, CONF2, with a sodium plenum and a lower blanket was established first and used as a basis for further studies in view of deterioration of safety parameters during reactor operation. Further options to study were an inner fertile blanket, introduction of moderator pins, a smaller core height, special designs for pins, such as 'empty' pins, and subassemblies. These special designs were proposed to facilitate melted fuel relocation in order to avoid core re-criticality under severe accident conditions. In the paper further CONF2 modifications are compared in terms of safety and fuel balance. They may bring further improvements in safety, but their accurate assessment requires additional studies, including transient analyses. Uncertainty studies were performed by employing a so-called Total Monte-Carlo method, for which a large number of nuclear data files is produced for single isotopes and then used in Monte-Carlo calculations. The uncertainties for the criticality, sodium void and Doppler effects, effective delayed neutron fraction due to uncertainties in basic nuclear data were assessed for an ESFR core. They prove applicability of the available nuclear data for ESFR optimization studies.