Recent studies suggest that Zero Boil-Off (ZBO) technologies, aimed at controlling the pressure inside cryogenic storage tanks, will play a prominant role in meeting NASA's future exploration goals. Small-scale experiments combined with validated and verified computational models can be used to optimize and then to scale up any future ZBO design. Since shortcomings in previous experiments make validating comprehensive two-phase flow models difficult at best; the Zero Boil-Off Tank (ZBOT) experiment has been proposed to fly aboard the International Space Station. In this paper, a numerical model has been developed to examine several test points in the ZBOT test matrix. Specifically, a numerical model is developed to evaluate four pressure control strategies after the tank undergoes a period of self-pressurization. The four strategies include axial liquid jet mixing, mixing provided by a sub-cooled liquid jet, bulk liquid cooling provided by a cold-finger and coldfinger cooling with axial jet mixing. Results indicate, that over the time scales under consideration, sub-cooled liquid jet mixing is the most effective means to reduce tank pressure.