The measurement of the Compton edge of the scattered electrons in GRAAL facility in European Synchrotron Radiation Facility (ESRF) in Grenoble with respect to the Cosmic Microwave Background dipole reveals up to 10 sigma variations larger than the statistical errors. We now show that the variations are not due to the frequency variations of the accelerator. The nature of Compton edge variations remains unclear, thus outlining the imperative of dedicated studies of light speed anisotropy.