We outline the strategy and constraints adopted for the design of medium-power lead-alloy-cooled actinide-burning reactors that strive for a lower cost than accelerator-driven systems and for robust safety. Reduced cost is pursued through the use of (1) a modular design and maximum power rating to capitalize on an economy of scale within the constraints imposed by modularity, (2) a very compact and simple supercritical-CO2 power cycle, and (3) simplifications of the primary system allowed by the use of lead coolant. Excellent safety is pursued by adopting the integral fast reactor approach of achieving a self-controllable reactor that responds to all key abnormal occurrences, including anticipated transients without scrams, by a safe shutdown without exceeding core integrity limits. The three concepts developed are the fertile-free actinide burner for incineration of all transuranics from light water reactor (LWR) spent fuel, the fertile-free minor actinide (MA) burner for preferential burning of MAs working in tandem with LWRs or gas-cooled thermal reactors, and the actinide burner with thorium fuel aimed also at reducing the electricity generation costs through longer-cycle operation.