A study is conducted to investigate conceptual liquid-metal reactor (LMR) core concepts, employing some unconventional design features for improved economics and safety. The unconventional design elements are used to supplement the conventional measures, which alone have apparently not led to an attractive LMR design for the 21st century. Better economics are obtained through simplicity and compactness of the core design. For simplicity, internal scattered blankets are omitted. Core compactness is achieved by maximum power flattening, resulting from axial and radial enrichment zones along with axial and radial (BeO) reflectors. To further enhance core compactness, the in-core control rods are replaced by reflector controls. For improved safety, the general objective is to reduce both coolant-void and burnup reactivities. However, even with the use of a wide spectrum of unconventional design features, such as burnable poisons, peripheral reflectors, and inner moderating regions, it is not possible to overcome the fact that both coolant-void and burnup reactivities cannot be reduced simultaneously to desirably low levels. The only resolution of this dilemma appears to be to minimize coolant-void reactivity and to “manage” the burnup reactivity losses, such that an accidental insertion of significant amounts of reactivity is mechanically not possible. A conceptual design with these characteristics is described.