The probability distribution in time at which the neutron population is a slightly supercritical system attains a prescribed level is considered for the case where a source injects well under one neutron per neutron lifetime. For the case of ramp insertion of reactivity it is shown that the energy released in the consequent burst of fissions may in some cases (e.g., unmoderated enriched uranium systems) exceed by over a factor of one hundred the energy release predicted by the reactor kinetics equations.