Abstract For a stochastic process reset at random times, we discuss to what extent the probabilities of some orderings of observables associated with the intervals of time between resetting events are universal, i.e. independent of the choice of the observables, and in particular, to what extent universality depends on the choice of the distribution of these intervals. For Poissonian resetting, universality relies only on a combinatorial argument and on the statistical properties of Poisson points. For a generic distribution of time intervals between resets, universality no longer holds in general.