The Doppler-deterioration of the energy resolution of conversion electrons emitted by fast moving nuclei has been mostly compensated by applying event-by-event kinematic corrections. The method has been applied to the scattering of 6 MeV/u 238U on 181Ta with Coulomb excitation of both the scattered projectiles and the recoiling target nuclei. The direction of flight of scattered projectiles and recoiling ejectiles were observed and registered in coincidence with conversion electrons emitted from Coulomb excited states. Assuming elastic (or quasi-elastic) scattering, the velocity of the electron-emitting nucleus and the subsequent shift in energy of the electron can be determined. This allows precise Doppler corrections for electrons emitted within a specific solid angle and observed by a system of four Mini-Orange spectrometers.