Can bank runs be avoided and should they be avoided? I analyze a banking environment where bank runs can occur as a result of negative signals about the bank's investments. In this environment, banks can make sure that runs do not occur by designing the deposit contract appropriately, I show that there are conditions under which it is profit-maximizing for the bank to avoid runs, and others under which occasional runs are part of optimal bank behavior. I also compare the banking arrangement to an arrangement based on trading in equity.