During the COVID-19 public health emergency (PHE), states were barred from disenrolling anyone from Medicaid unless the beneficiary asked to be disenrolled, moved out of state, or died. Coverage increased, but as the PHE ends an estimated 7 million eligible Americans are expected to lose insurance due to difficulty navigating the renewal process. The end of the PHE therefore offers state policymakers a chance to reassess the value of such administrative burdens as a variety of policy tools are available to mitigate these losses. We inform this discussion via a national survey that captures public preferences around administrative burdens in public health insurance. We find strong public support for burden reduction techniques that minimize coverage losses such as using administrative data to shift burdens onto the state and better outreach and communication, with an average of 74 percent of respondents supporting each policy tool. This support holds across the ideological spectrum, demographic groups, but it is stronger among liberals than conservatives, for those with more direct experience of burdens, those who struggle with such burdens, and for those with lower racial prejudice.