Motivated by a need in online advertising, where control systems often involve estimators of very small event rates, we propose an adaptive algorithm that regulates the stiffness of an otherwise time-invariant Bayesian event rate estimator to maintain a desired relative steady-state standard deviation of the event rate estimate. The result is an estimator that is fast (agile) when permitted by the observed input data, and that is slow (stiff) only when necessary to maintain the desired relative steady-state standard deviation of the estimate.