  We investigate the relaxation of long-tailed distributions under stochastic
dynamics that do not support such tails. Linear relaxation is found to be a
borderline case in which long tails are exponentially suppressed in time but
not eliminated. Relaxation stronger than linear suppresses long tails
immediately, but may lead to strong transient peaks in the probability
distribution. A delta function initial distribution under stronger than linear
decay displays not one but two different regimes of diffusive spreading.
