We build a model of a financial intermediary, in the tradition of Diamond and Dybvig (1983), and show that allowing the intermediary to impose redemption fees or gates in a crisis—a form of suspension of convertibility—can lead to preemptive runs. In our model, a fraction of investors (depositors) can become informed in advance about a shock to the return on the intermediary’s assets. Later, the informed investors learn the realization of the shock and choose their redemption behavior based on this information. We prove two results: First, there are situations in which informed investors would wait until the uncertainty is resolved before redeeming if redemption fees or gates cannot be imposed, but those same investors would redeem preemptively if fees or gates are possible. Second, we show that for the intermediary, which maximizes the expected utility only of its own investors, imposing gates or fees can be ex post optimal. These results have important policy implications for intermediaries that are vulnerable to runs, such as money market funds, because the preemptive runs that can be caused by the possibility of gates or fees may have damaging negative externalities.