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Recent observations of transient radio impulses by an Earth-orbiting satellite appear to be quite unlike any previously reported. They appear as pairs of brief (a few microseconds), noiselike bursts, separated by a few tens of microseconds, and are dispersed in a way that implies subionospheric origin. Over 300 of these events have now been observed. These “transionospheric pulse pairs” (TIPPs) have not yet been associated with any known source, although thunderstorms are suspected. The observations, made by the Blackbeard instrument on the ALEXIS satellite, are digitized records of the electric field in a passband from about 25 to 100 MHz. Ground-based observations of lightning in this band appear quite different, even accounting for ionospheric dispersion: bursts of short pulses last hundreds of microseconds and have much lower power (when propagated to the satellite) than TIPP events. Signals that resemble the ground-based data have been observed by Blackbeard but, being much weaker, are much less likely to trigger the instrument than are the strong pulse pair events. In this paper we analyze 97 of the early TIPP observations. We compute several parameters that describe the events: the location of the satellite at the time of reception, the energy in each pulse, the separation between pulses, the duration of each pulse, and the dispersion of each pulse. The statistical distributions of these parameters provide clues to and constraints on possible source mechanisms. The possibility that the pulses might be the direct and reflected signals from a high-altitude source is considered and cannot be rejected by the data.