In the existing literature, panic-based bank runs are triggered by a commonly acknowledged and observed sunspot signal. There are only two equilibrium realizations resulting from the commonly observed sunspot signal: Everyone runs or no one runs. I consider a more general and more realistic situation in which consumers observe noisy private sunspot signals. If the noise in the signals is sufficiently small, there exists a proper correlated equilibrium for some demand deposit contracts. A full bank run, a partial bank run (in which some consumers panic whereas others do not), or no bank run occurs, depending on the realization of the sunspot signals. If the probabilities of runs are small, the optimal demand deposit contract tolerates full and partial bank runs.