A bioabsorbable wire material includes manganese (Mn) and iron (Fe). One or more additional constituent materials (X) are added to control corrosion in an in vivo environment and, in particular, to prevent and/or substantially reduce the potential for pitting corrosion. For example, the (X) element in the Fe—Mn—X system may include nitrogen (N), molybdenum (Mo) or chromium (Cr), or a combination of these. This promotes controlled degradation of the wire material, such that a high percentage loss of material the overall material mass and volume may occur without fracture of the wire material into multiple wire fragments. In some embodiments, the wire material may have retained cold work for enhanced strength, such as for medical applications. In some applications, the wire material may be a fine wire suitable for use in resorbable in vivo structures such as stents.