Compact tokamak fusion reactors utilizing advanced high-temperature superconducting magnets for the toroidal field coils have received considerable recent attention due to the promise of more compact devices and more economical fusion energy development. Facilities with combined Fusion Nuclear Science (FNS) and Pilot Plant missions to provide both the nuclear environment needed to develop fusion materials and components while also potentially achieving sufficient fusion performance to generate modest net electrical power are considered. The performance of the tokamak fusion system is assessed using a range of core physics and toroidal field magnet performance constraints to better understand which parameters most strongly influence the achievable fusion performance.