  For each of (i) arbitrary stochastic reset, (ii) deterministic reset with
arbitrary period, (iii) reset at arbitrary constant rate, and then in the sense
of either (a) first-order stochastic dominance or (b) expectation (i.e. for
each of the six possible combinations of the preceding), those laws of random
times are precisely characterized that are rendered no bigger [rendered no
smaller; left invariant] by all possible restart laws (within the classes (i),
(ii), (iii), as the case may be). Partial results in the same vein for reset
with branching are obtained. In particular it is found that deterministic and
arbitrary stochastic restart lead to the same characterizations, but this
equivalence fails to persist for exponential (constant-rate) reset.
