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Magnetic surveys are quite successful at locating buried steel objects, including unexploded ordnance (UXO). However, many of the anomalies apparent in a magnetic image of a contaminated area are from metallic debris, shrapnel, and geological variations in ferromagnetic concentration. Observations are usually made in the far-field of the object so that, in most cases, we can only recover the dipole moment of a buried item. Due to self-demagnetization effects, the magnitude and direction of induced magnetism varies significantly with ordnance orientation. This results in an infinite number of ordnance-like objects that can reproduce a given dipole moment. To discriminate, we define a library of ordnance items expected to occur in the area and find how closely each recovered moment matches one of the UXOs in this library. We define the size of this mismatch as the remanent magnetization and produce a prioritized dig-list on the assumption that items with lower remanence are more likely to be UXO. Such a ranking scheme proves to be very effective when implemented at two sites in Montana. The analysis reveals that live-site and emplaced UXO have significantly different remanence and implies that previous tests of magnetic discrimination performance on seeded sites have been overly pessimistic.