A bioerodible endoprosthesis includes a bioerodible body including an alloy comprising at least 85 weight percent magnesium and at least one high-melting-temperature element having a melting temperature of greater than 700° C. The alloy has a microstructure including equiaxed magnesium-rich phase grains and optionally high-melting-temperature intermetallic phases. The equiaxed magnesium-rich phase grains have an average grain diameter of less than or equal to 10 microns. High-melting-temperature intermetallic phases, if present, can have an average longest dimension of 3 microns or less.