We study a run on uninsured deposits in Danish banks triggered by a reform that limited deposit insurance coverage. Using a unique dataset with information about all individual bank accounts, we show that the reform caused a 50% decrease in deposits above the insurance limit in non-systemic banks, but a much smaller decrease in systemic banks which experienced less withdrawals of uninsured balances, but also more openings of new uninsured accounts. The differential reallocation of uninsured deposits highlights the destabilizing effects of banks that are too-big-to-fail and the important role of deposit insurance in mitigating this financial fragility.