  Self-averaging of singular thermodynamic quantities at criticality for
randomly and thermally diluted three dimensional Ising systems has been studied
by the Monte Carlo approach. Substantially improved self-averaging is obtained
for critically clustered (critically thermally diluted) vacancy distributions
in comparison with the observed self-averaging for purely random diluted
distributions. Critically thermal dilution, leading to maximum relative
self-averaging, corresponds to the case when the characteristic vacancy
ordering temperature is made equal to the magnetic critical temperature for the
pure 3D Ising systems. For the case of a high ordering temperature, the
self-averaging obtained is comparable to that in a randomly diluted system.
