The magnetic detection of objects with ferromagnetic casings, such as unexploded ordnance (UXO), is typically plagued by high false alarm rates. In the past, only estimates of the magnitudes of the dipoles found in a magnetic search have been used to determine if the dipoles are UXO-like. Following Altshuler, this paper reports on a method aimed at significantly reducing the false-alarm rate, thereby making magnetic detection of UXO more effective. The method assumes that UXO magnetic dipoles are predominantly induced, rather than permanent, and that their ferromagnetic casings can be closely approximated as spheroids. the method relies on the determination of the full magnetic moment of each magnetic dipole. This information can be obtained, even in a multi-target scenario, by magnetic field gradiometers, which measure the five independent components of the gradient of the magnetic field. Two distinct two-parameter classification schemes are described. One assumes that the magnetic object is lying flat and determines the effective magnetic susceptibilities parallel and normal to the symmetry axis. The other scheme makes no assumption about the orientation of the magnetic object, but provides simple and robust limits on moment magnitude and direction that effectively reject clutter. Real magnetic clutter data gathered at sea is employed to demonstrate and estimate the effectiveness of these schemes.