We examine data from the Electron/Proton Angle Spectrometer instrument, also known as Medium Energy B, flown on the CRRES satellite (July 1990 to August 1991). Because of its strongly eccentric orbit, CRRES can detect substorm onsets in the region L=4 to L=8, covering the time sectors 1600--0800 MLT. Substorm onsets which are virtually dispersionless in energy have commonly been associated with acceleration processes which occur in the immediate vicinity of the satellite. Data from CRRES show that such virtually dispersionless onsets can occur far in the inner magnetosphere down to L=4.3 and are distributed up to ¿5 hours around local magnetic midnight. Results from a statistical study are presented. We develop a method of using single-satellite measurements of near-dispersionless substorm onsets, together with the observed ''drift echoes'' of these injections, to establish a ''source region'' for the energetic particles observed at onset. This method is here applied to electrons only. A database of model drift paths has been set up and is used to calculate the possible interceptions between drift paths of various energies from a source region with the satellite trajectory. Our results indicate that the source region can have a sharp boundary in MLT and can extend over several RE. For some events it is possible to deduce an outer radial limit for the injection region, favoring a more local substorm onset mechanism. Our modeling further shows that the injection and drift echo signature observed at the satellite is quite insensitive to the actual shape of the injection boundary. ¿ American Geophysical Union 1996