We have performed a theoretical study of three polymorphs of Pb-supersaturated Sn-rich Pb-Sn alloys with the -Sn, -Sn, and a simple-hexagonal -Sn structure employing quantum-mechanical calculations. We focused on structure–property relations in the case of lattice parameters, thermodynamic stability, elastic properties, and mechanical stability as well as electronic-structure density of states. Compositional trends in structural, thermodynamic, and electronic properties were found nearly linear. Our study also sheds new light on a decades-long controversy surrounding the existence of -phase and -phase supersaturated Sn-rich Pb-Sn alloys. We suggest that the experimental difficulties when synthesizing them are caused by their high formation energy and mechanical instability of the -phase.