The tumor-suppressive transcription factor p53 is a master regulator of stress responses. In non-stressed conditions, p53 is maintained at low levels by the ubiquitin ligase Mdm2 and its binding partner Mdmx. Mdmx depletion leads to a biphasic p53 response, with an initial post-mitotic pulse followed by oscillations. The mechanism underlying this dynamical behavior is unknown. Two different roles for Mdmx have been proposed: enhancing p53 ubiquitination by Mdm2 and inhibiting p53 activity. Here, we developed a mathematical model of the p53/Mdm2/Mdmx network to investigate which Mdmx functions quantitatively affect specific features of p53 dynamics under various conditions. We found that enhancement of Mdm2 activity was the most critical role of Mdmx under unstressed conditions. The model also accurately predicted p53 dynamics in Mdmx-depleted cells following DNA damage. This work outlines a strategy for rapidly testing possible network interactions to reveal those most impactful in regulating the dynamics of key proteins.