We searched for gamma-ray emission from lightning using the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) satellite by identifying times when RHESSI was near over 2 million lightning discharges localized by the Worldwide Lightning Location Network (WWLLN). We then stacked together the gamma-ray arrival times relative to the sferic times, correcting for light propagation time to the satellite. The resulting stacked gamma-ray time profile is sensitive to an average level of gamma-ray emission per lightning discharge far lower than what can be recognized above background for a single terrestrial gamma-ray flash (TGF). The summed signal from presumed small, previously unknown TGFs simultaneous with WWLLN discharges is remarkably weak: for the region from 0 to 300 km beneath RHESSI's footprint, (6.2 ± 3.8) × 10−3 detector counts/discharge are measured, as opposed to a typical range of 12–50 detector counts for TGFs identified solely from the gamma-ray signal. Under the assumption of a broken power law differential distribution of TGF intensities, we find that the index must harden dramatically or cut off just below the sensitivity limit of current satellites and that for most scenarios less than 1% of lightning can produce a TGF that belongs anywhere in the same distribution as those that are observable. For the minority of scenarios where more than a few percent of flashes produce a TGF, most of these “TGFs” are less than 10−4 of the luminosity of the faintest RHESSI TGFs and therefore closer to the luminosity of lightning stepped leaders. The rarity of TGFs holds not only for TGFs simultaneous with the sferic observed by WWLLN but also for any time within 10 ms of the sferic, allowing (for example) for the possibility that different events within the upward propagation of a negative leader in positive intracloud lightning triggered the TGF and WWLLN's detection.