Fertile-free fast lead-cooled modular reactors are proposed as efficient incinerators of plutonium and minor actinides (MAs) for application to advanced fuel cycles devoted to transmutation. Two concepts are presented: (1) an actinide burner reactor, designed to incinerate mostly plutonium and some MAs, and (2) a minor actinide burner reactor, devoted to burning mostly minor actinides and some plutonium. These transuranics are loaded in a fertile-free Zr-based metallic fuel to maximize the incineration rate. Both designs feature streaming fuel assemblies that enhance neutron leakage to achieve favorable neutronic feedback and a double-entry control rod system that reduces reactivity perturbations during seismic events and flattens the axial power profile. A detailed neutronic analysis shows that both designs have favorable neutronic characteristics and reactivity feedback mechanisms that yield passive safety features comparable to those of the Integral Fast Reactor. A safety analysis presents the response of the burners to anticipated transients without scram on the basis of (1) the integral parameter approach and (2) simulations of thermal-hydraulic accident scenario conditions. It is shown that both designs have large thermal margins that lead to safe shutdown without structural damage to the core components for a large spectrum of unprotected transients. Furthermore, the actinide destruction rates are comparable to those of the accelerator transmutation of waste concept, and a fuel cycle cost analysis shows the potential for economical accomplishment of the transmutation mission compared to other proposed actinide-burning options.