A decision-theoretical model for seismic discrimination between earthquakes and underground nuclear explosions is developed. The influence of long- and short-period detection thresholds on the probabilities to identify explosions and to make false alarms is discussed. The model includes identification by negative evidence. This kind of identification is considered in the case when only short-period data are available and when the long-period signal amplitude is supposed to be less than or equal to the seismic noise amplitude. For one set of data—obtained from North American events at the Hagfors Observatory in Sweden—the applicability of the m(M)-method is increased about half a magnitude by including identification by negative evidence.