Supercritical CO2 (s-CO2) operated in a closed-loop Brayton cycle offers the potential of higher cycle efficiency versus superheated or supercritical steam cycles at temperatures relevant for concentrating solar power (CSP) applications. Brayton-cycle systems using s-CO2 have a smaller weight and volume, lower thermal mass, and less complex power blocks versus Rankine cycles due to the higher density of the fluid and simpler cycle design. The simpler machinery and compact size of the s-CO2 process may also reduce the installation, maintenance, and operation cost of the system. In this work we explore s-CO2 Brayton cycle configurations that have attributes that are desirable from the perspective of a CSP application, such as the ability to accommodate dry cooling and achieve greater than 50% efficiency, as specified for the U.S. Department of Energy SunShot goal. Recompression cycles combined with intercooling and/or turbine reheat appear able to hit this efficiency target, even when combined with dry cooling. In addition, the intercooled cycles expand the temperature differential across the primary heat exchanger, which is favorable for CSP systems featuring sensible-heat thermal energy storage.