Theoretical understanding of regional P/S discriminants has been a long- standing research topic with important implications for nuclear explosion monitoring. The observation that discrimination is poor at low frequencies, but becomes significant at higher frequencies, usually at about 3 to 4 Hz, particularly needs understanding. To gain insight, source and attenuation models are used to predict spectra of regional seismic phases (Pn, Sn, and Lg) for nuclear explosions and selected earthquakes near the Lop Nor, Semipalatinsk (Balapan and Degelen Mountain), and Novaya Zemlya test sites in China and the former Soviet Union. A modified Brune (1970) model (à la Walter and Taylor, 2002) is used to predict P- and S-source terms for earthquakes. A Mueller/Murphy (1971) model is used for explosions, including a new conjecture that the S waves may be modeled by the same functional form as for P waves, but with corner frequency reduced by the ratio of near-source shear and compressional velocities, vs(S)/vs(P). Results indicate that the frequency dependence of Pn/Sn and Pn/Lg discrimination performance at all of these hard-rock test sites is primarily due to differences in the corner frequencies of P and S waves for explosions, qualitatively consistent with observations by Xie and Patton (1999) for Lop Nor. P/S discrimination emerges at the explosion S-wave corner frequency and does not improve above the P-wave corner frequency. Scaling of the explosion S-wave corner frequency with elastic radius as vs(S)/Re at all of these test sites suggests that major contributions to S-wave generation from explosions may be occurring at the same distance scale (i.e., the elastic radius) as P waves from explosions. The explicit physical mechanism of this near-source S-wave generation is still being investigated. Implications regarding application of regional P/S discriminants are discussed.