In this study, the characteristics of changes in reactivity due to increasing burnup of uranium-fueled fast reactors are analyzed. A new classification system for nuclear reactor cores based on their uncontrolled tendency for reactivity changes during burnup was introduced and the design-optimization strategy for any fast reactor core aimed at a minimized reactivity swing is outlined. The 235U feed-fuel enrichment level that minimizes the burnup reactivity swing of a sodium-cooled metallic-fueled core is 10% to 12.5% for an average target fuel burnup of 1% to 20% FIMA (fission of initial metal atom). The higher the target burnup of the system, the lower the feed-fuel enrichment level that minimizes swing. The minimum attainable swing for a 125-MW(thermal) metallic-fueled sodium-cooled core is found to be ∼200 pcm for 5% FIMA burnup and increases to ∼800 pcm for a system aiming at 10% FIMA. In general, if the target discharge burnup is doubled, the minimum attainable burnup reactivity swing quadruples. Any optimized minimum reactivity swing core will form a positive parabolic uncontrolled reactivity trajectory with burnup, where the beginning of cycle and end of cycle reactivities are equal. Uranium-fueled fast cores with minimized burnup reactivity swing are net consumers of fissile material, with a fissile conversion ratio in the range of 0.7 to 0.9.