The radiative process responsible for gamma-ray burst (GRB) prompt emission has not been identified yet. If dominated by fast-cooling synchrotron radiation, the part of the spectrum immediately below the nF n peak energy should display a power-law behavior with slope a2 = -3 2, which breaks to a higher value a1 = -2 3 (i.e., to a harder spectral shape) at lower energies. Prompt emission spectral data (usually available down to ∼10 20 keV) are consistent with one single power-law behavior below the peak, with typical slope a = -1, higher than (and then inconsistent with) the expected value α2= -3 2. To better characterize the spectral shape at low energy, we analyzed 14 GRBs for which the Swift X-ray Telescope started observations during the prompt. When available, Fermi-GBM observations have been included in the analysis. For 67% of the spectra, models that usually give a satisfactory description of the prompt (e.g., the Band model) fail to reproduce the 0.51000 keV spectra: lowenergy data outline the presence of a spectral break around a few keV. We then introduce an empirical fitting function that includes a low-energy power law a1, a break energy Ebreak, a second power law α2, and a peak energy Epeak. We find σ1 = -0.66 (s = 0.35), log keV 0.63 ( ) Ebreak = (s = 0.20), σ2 = -1.46 (s = 0.31), and log keV 2.1 (Epeak) = (s = 0.56). The values σ1 and σ2 are very close to expectations from synchrotron radiation. In this context, Ebreak corresponds to the cooling break frequency. The relatively small ratio Epeak break E ∼ 30 suggests a regime of moderately fast cooling, which might solve the long-lasting problem of the apparent inconsistency between measured and predicted low-energy spectral index.