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Lightweight, recyclable, and plentiful Mg alloys are receiving increased attention due to an exceptional combination of strength and ductility not possible from pure Mg. Yet, due to their alloying elements, such as rare-earths or aluminum, they are either not economical or biocompatible. Here we present a new rare-earth and aluminum-free magnesium-based alloy, with trace amounts of Zn, Ca, and Mn (≈ 2% by wt.). We show that the dilute alloy exhibits outstanding high strength and high ductility compared to other dilute Mg alloys. By direct comparison with annealed material of the same chemistry and using transmission electron microscopy (TEM), high-resolution TEM (HR-TEM) and atom probe tomography analyses, we show that the high strength can be attributed to a number of very fine, Zn/Ca-containing nanoscale precipitates, along with ultra-fine grains. These findings show that forming a hierarchy of nanometer precipitates from just miniscule amounts of solute can invoke simultaneous high strength and ductility, producing an affordable, biocompatible Mg alloy.