Using an AFM-based instrumented nanoindentation system, the nanoindentation response of γ′ particles (Ni3Al) in a Ni-base single crystal superalloy CMSX-4 was characterized to demonstrate the influence of the softer γ matrix on the measurement of nano-mechanical properties of γ′ particles. The properties of the γ′ particles were measured after both a standard and a coarsening heat treatment, in which the initially sub-micron sized cuboidal γ′ particles transformed to large, irregularly shaped γ′ precipitates with dimensions in excess of 30 urn. The measured nano-hardness of the coarsened γ′ precipitates in CMSX-4 appears to increase slightly with the increasing load. Nano-compression testing of cuboidal γ′ particles, electrolytically extracted from a CMSX-4 after a standard solution and age heat treatment, was also performed. With a maximum value of 10 GPa, the measured yield stress of these dislocation-free γ′ particles approaches the ideal strength and is equivalent to -G/17. Compared to the measured yield strengths of γ′ phase in its bulk crystal form, these nano-compression results are more than a factor of 33 higher. Additionally, the 'softening' effect of Ga+ ion implantation on the strength of dislocation-free nanocrystals was also assessed. The resulting yield strengths of cuboidal γ′ precipitates imaged with a focused ion beam were at least 5 GPa lower than those that had not been subjected to Ga+ ion implantation.