The aim of this article is to describe the design strategy deployed in developing new bioabsorbable Mg–Y–Zn alloys. The development approach is based on a microalloying concept, which aims to restrict grain growth considerably during alloy casting and forming. We discuss the efficiency of the design approach, and evaluate the characteristics of the new alloys using metal-physical experiments, thermodynamic calculations, and TEM analysis. Our results show that after extrusion the alloys have very fine grains (<10m), exhibit high ductility (uniform elongation: 17–20%) at considerable strength (ultimate tensile strength: 250–270 MPa), and reveal the presence of finely distributed intermetallic particles, which are stable upon annealing. Due to an attractive combination of mechanical, electrochemical and biological properties, the new alloys are very promising not only for applications in medicine but also in other fields.