 It ought to be stressed that there is nothing in the GRW theory which forbids or makes problematic to assume that the localization function has compact support, but it also has to be noted that following this line would be totally useless: since the evolution equation contains the kinetic energy term, any function, even if it has compact support at a given time, will instantaneously spread, acquiring a tail extending over the whole space. If one sticks to the probabilistic interpretation and one accepts the completeness of the description of the states of physical systems in terms of the wave function, the tail problem cannot be avoided.