We examine heterogeneity in depositor responses to solvency risk using depositor‐level data for a bank that faced two different runs. We find that depositors with loans and bank staff are less likely to run than others during a low‐solvency‐risk shock, but are more likely to run during a high‐solvency‐risk shock. Uninsured depositors are also sensitive to bank solvency. In contrast, depositors with older accounts run less, and those with frequent past transactions run more, irrespective of the underlying risk. Our results show that the fragility of a bank depends on the composition of its deposit base.