In the present study, lap joints of dissimilar 5052 aluminum alloy and pure copper were fabricated by friction stir spot welding process. The work was aimed to find simultaneous effect of parameters such as tool rotary speed (1000, 1500, and 2000 rpm) and dwell time (5, 10, and 15 s) on lap shear force (LSF), hardness, and microstructure evolution. Also, statistical models of the quality characteristics were developed to understand which parameter has dominant effect on quality characteristics. Research findings showed that to obtain sound joints with high lap shear strength, tool rotary speed of 1500 rpm and dwell time of 15 s should be selected. It provides sufficient heat input for mechanical interlocking and prevents the formation of coarse and thick intermetallic compounds (IMCs) in the stir zone. On the other hand, to achieve maximum hardness, 2000 rpm tool rotary speed should be chosen to provide enough heat for formation of intermetallic compound and 10Â s dwell time should be used to prevent enough time for microstructure refining. Moreover, from the statistical analyses, it was found that dwell time and tool speed are the significant factors for lap shear strength and hardness, respectively. In order to attain simultaneous maximum strength and hardness, tool speed of 1630 rpm and dwell time of 14 s should be used. In such condition, lap shear strength of 1980 N and hardness of 78 V are achieved with desirability of 86%.