We report on three classes of terrestrial gamma-ray flashes (TGFs) from the Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI) satellite. The first class drives the detectors into paralysis, being observed usually through a few counts on the rising edge and the later tail of Comptonized photons. These events – and any bright TGF – reveal their true luminosity more clearly via their Compton tail than via the main peak, since the former is unaffected by the unknown beaming pattern of the unscattered radiation, and Comptonization mostly isotropizes the flux. This technique could be applied to TGFs from any mission. The second class is more than usually bright and long in duration. When the magnetic field at the conjugate point is stronger than at the nearby footpoint, we find that 4 out of 11 such events show a significant signal at the time expected for a relativistic electron beam to make a round trip to the opposite footpoint and back. We conclude that a large fraction of TGFs lasting more than a few hundred microseconds may include counts due to the upward-moving secondary particle beam ejected from the atmosphere. Finally, using a new search algorithm to find short TGFs in RHESSI, we see that these tend to occur more often over the oceans than land, relative to longer-duration events. In the feedback model of TGF production, this suggests a higher thunderstorm potential, since more feedback per avalanche implies fewer “generations” of avalanches needed to complete the TGF discharge.