Determining whether a seismic event is an earthquake, explosion, collapse, or something more complex can be done using regional (Δ<13°) intermediate‐period (T>10 s) full waveform moment tensors down to low magnitudes (M∼3.5). The moment tensor results can be improved for sparse station configurations when teleseismic (Δ>30°) array‐based short‐period (T<1 s) P constraints are added. The inclusion of teleseismic‐P aids in event discrimination because it samples the lower region of the focal‐sphere, a region where intermediate‐period waveforms recorded at the surface have low‐sensitivity for shallow event depths. The teleseismic‐P constraint is particularly useful in reducing the trade‐off between a shallow explosion and a shallow volume‐compensated linear‐vector dipole with a vertical axis in compression. This trade‐off can complicate discrimination. The teleseismic‐P constraint is applied to the source‐type analysis of the announced nuclear test of the Democratic People’s Republic of Korea on 25 May 2009, resulting in greater confidence in a dominantly explosive solution.