<p>The microstructure of electronic solder joints is created by solidification in an undercooled melt. Here, we apply the framework of solidification microstructure selection maps (SMSMs) to Sn-Ag solder balls with compositions from 0.5 to 5.0 wt.% Ag and bulk undercoolings in the range 10–70 K. The effects of Ag and melt undercooling on the transition from single-grain to cyclic-twinned microstructures and the extent of interlacing are revealed. Controlled by the Ag content and the competitive nucleation between the β-Sn and Ag₃Sn phases, a competition between tin dendrite and eutectic growth is observed that decides the microstructure of solder balls. The solidification microstructure selection map, modified to account for whether Ag₃Sn or β-Sn nucleate first in competitive nucleation, is in reasonable agreement with coupled zone theory. The map provides a guide for tailoring desired solder microstructures for mechanical performance through controlling the nucleation undercooling of β-Sn and Ag₃Sn during solidification.</p>