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 νF ν peak energy should display a power-law behavior with slope α 2 = −3/2, which breaks to a higher value α 1 = −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 α = −1, higher than (and then inconsistent with) the expected value α 2 = −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 in reproducing the 0.5 − 1000 keV spectra: low-energy 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 α 1 , a break energy E break , a second power law α 2 , and a peak energy E peak . We find α 1 = −0.66 (σ = 0.35), log(E break /keV) = 0.63 (σ = 0.20), α 2 = −1.46 (σ = 0.31), and log(E peak /keV) = 2.1 (σ = 0.56). The values α 1 and α 2 are very close to expectations from synchrotron radiation. In this context, E break corresponds to the cooling break frequency. The relatively small ratio E peak /E break ∼ 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.