We demonstrate that a bank can offer demand deposits and yet avoid bank runs without deposit insurance if it also offers time deposits that have a low liquidation value. Self-fulfilling runs do not occur, as maturity mismatch is eliminated. To do this, we modify DIAMOND AND DYBVIGs [1983] model so that depositors have differing risks of encountering a preference shock. We show that high-risk depositors will hold their savings as demand deposits, whereas low-risk depositors will prefer time deposits. These deposit choices transfer liquidity optimally from low-risk to high-risk depositors, who place the highest value on liquidity.