The new Tokamak Systems Code, used to investigate compact ignition tokamaks (CITs), can simultaneously vary many parameters, satisfy many constraints, and minimize or maximize a figure of merit. It is useful in comparing different CIT design configurations over wide regions of parameter space and in determining a desired design point for more detailed physics and engineering analysis, as well as for performing sensitivity studies for physics or engineering issues. Operational windows in major radius (R) and toroidal field (B) space for fixed ignition margin are calculated for the Ignifed and Inconel candidate CITs. The minimum R bounds are predominantly physics limited, and the maximum R portions of the windows are engineering limited. For a modified Kaye-Goldston plasma energy confinement scaling, the minimum size is 1.15 m for the Ignifed device and 1.25 m for the Inconel device. With the Ignition Technical Oversight Committee physics guidance of B2a/q* and Ip > 10 MA, the Ignifed and baseline Inconel devices have minimum sizes of 1.2 and 1.25 m and toroidal fields of 11 and 10.4 T, respectively. Sensitivity studies show Ignifed to be more sensitive to coil temperature changes than the Inconel device, whereas the Inconel device is more sensitive to stress perturbations.