The long-lasting tension between the observed spectra of gamma-ray bursts (GRBs) and the predicted synchrotron emission spectrum might be solved if electrons do not completely cool. Evidence of incomplete cooling was recently found in Swift GRBs with prompt observations down to 0.1 keV, and in one bright Fermi burst, GRB 160625B. Here we systematically search for evidence of incomplete cooling in the spectra of the ten brightest short and long GRBs observed by Fermi. We find that in eight out of ten long GRBs there is compelling evidence of a low-energy break (below the peak energy) and good agreement with the photon indices of the synchrotron spectrum (respectively −2/3 and −3/2 below the break and between the break and the peak energy). Interestingly, none of the ten short GRBs analysed shows a break, but the low-energy spectral slope is consistent with −2/3. In a standard scenario, these results imply a very low magnetic field in the emission region (B′∼10 G in the comoving frame), at odd with expectations.