This paper (i) investigated how the microstructure, conductivity, and mechanical properties of Cu-7Cr-0.1Ag microcomposites were changed by cold drawing and subsequent heat treatment, and (ii) produced the Cu-7Cr-0.1Ag microcomposite with an optimum combination of strength and conductivity. The figure of merit Z (combining strength and conductivity) of the Cu-7Cr-0.1Ag microcomposite was larger than that of the microcomposite without silver for each heat treatment. The value of Z of the Cu-7Cr-0.1Ag microcomposite was a maximum after heat treatment for 1 h at 600 °C, indicating that this was the optimum intermediate heat treatment. The following combinations of conductivity, strength and ductility (measured as elongation to fracture) were obtained by the Cu-7Cr-0.1Ag microcomposite with η = 8: (i) 77.9% IACS (International Annealed Copper Standard), 920 MPa and 3.1%; (ii) 79.3% IACS, 880 MPa and 3.3%; and (iii) 79.9% IACS, 798 MPa and 3.5%. These values for the Cu-7Cr-0.1Ag microcomposite were larger than those of the Cu-7Cr microcomposite.