Some novel high conductivity–high strength materials were designed in the binary Cu–Mg. They exhibit an excellent balance between strength and electrical properties. The properties and the performance of the designed materials are compared with the main Cu-based alloys and the analysis shows that they perform equally to the best one (Cu–Be). Furthermore, we show that an increase of Mg content modifies the microstructure feature and leads to a strong increase of strength without any significant deterioration of the electrical conductivity. This behavior was attributed to the formation of eutectic islands in which high density of Cu2Mg nanoparticles precipitate.