  Restart -- interrupting a stochastic process followed by a new start -- is
known to improve the mean time to its completion, and the general conditions
under which such an improvement is achieved are now well understood. Here, we
explore how restart affects other important metrics of first-passage phenomena,
namely the median and the mode of the first-passage time distribution. Our
analysis provides a general criterion for when restart lowers the median time,
and demonstrates that restarting is always helpful in reducing the mode.
Additionally, we show that simple non-uniform restart strategies allow to
optimize the mean and the median first-passage times, regardless of the
characteristic time scales of the underlying process. These findings are
illustrated with the canonical example of a diffusive search with resetting.
