In a previous paper (Phys. Rev. E 1995, 52, 2198) we proposed that the fluctuation amplitudes of equilibrium systems are minimal relative to nearby dissipative nonequilibrium states. This behavior was found in nonequilibrium molecular dynamics calculations at fixed density and kinetic temperature. In this paper we examined this rule at fixed internal energy (microcanonical ensemble) and also for two-dimensional systems. We find that the extremum behavior remains valid despite the change in boundary conditions and system dimensionality.