Although the maximal strength of Cu with a mean grain size of 10 nm has been reported as ∼1000 MPa, the maximal strength of nanostructured Cu processed by severe plastic deformation (SPD) is ∼450 MPa, owing to the saturation of accumulated strain caused by recovery or recrystallization during the SPD process. The strength of SPD-processed Cu can be increased by adding solid-solution atoms. A significant increase in the strength of nanostructured Cu after adding a small amount of Si solute atoms was reported in our previous study. In this study, various-composition Cu–Zn, Cu–Si, and Cu–Ni solid-solution alloys were subjected to high-pressure torsion (HPT) processing, which is one of the SPD processes. To reveal the role of solid-solution atoms on the deformation of Cu during the SPD process, the effects of Zn, Si, and Ni additions on hardness and microstructure of Cu after various HPT rotations were systematically investigated, up to the solubility limits of these atoms. It is well known that Zn and Si atoms decrease the stacking fault energy (SFE) of Cu. On the other hand, Ni atoms have the opposite effect to that of Zn and Si on the SFE of Cu. Experimental results were considered in terms of the atomic concentration of solute atoms ca, electron-atom ratio e/a, and the SFE. The hardness of 140 HV of the nanostructured Cu significantly increased with increasing addition of Zn, Si, and Ni. The maximal hardness values of the nanostructured Cu–Zn, Cu–Si, and Cu–Ni alloys were 250 HV (29.4 at%Zn), 275 HV (4.5 at%Si), and 360 HV (81.4 at%Ni), respectively. In the case of the nanostructured Cu–Zn and Cu–Si alloys, the hardness increase correlated with the reduction in the SFE as a function of e/a. The decreased SFE by Zn and Si additions increased strain hardening during the SPD process. This strengthened the nanostructured Cu–Zn and Cu–Si alloys. On the other hand, hardening of the nanostructured Cu–Ni alloys is related not to the SFE changes, but to dislocation pinning or dragging by Ni solute atoms followed by suppression of recovery or recrystallization during the SPD process. This Paper was Originally Published in Japanese in J. Japan Inst. Copper 57 (2018) 286–290.