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The nickel-base alloy NIMONIC PE16 is strengthened by coherent spherical nano-scale precipitates of the L12-long range ordered γ′-phase. Along grain boundaries precipitate free zones (PFZs) may form, which lower the yield strength drastically. In this study it has been attempted to eliminate this softening effect by double aging treatments: the main γ′-precipitate dispersion is grown at 1079 K and subsequently finer γ′-particles are precipitated at 949 K – in between the larger 1079 K-γ′-precipitates and in the PFZs formed at 1079 K. Unfortunately softening by PFZs could not be suppressed by these procedures. In addition, multiple strengthening of finely grained, PFZ-free NIMONIC PE16-polycrystals by γ′-precipitates, by atoms dissolved in the matrix, and by grain boundaries has been modeled and computer simulated.