We reconsider the QCD predictions for the radiative decay B -> gamma lv(l) with an energetic photon in the fi nal state by taking into account the 1/E-gamma, 1/m(b) power-suppressed hard-collinear and soft corrections from higher-twist B-meson light-cone distribution amplitudes (LCDAs). The soft contribution is estimated through a dispersion relation and light-cone QCD sum rules. The analysis of theoretical uncertainties and the dependence of the decay form factors on the leading-twist LCDA phi+(omega) shows that the latter dominates. The radiative leptonic decay is therefore well suited to constrain the parameters of phi+(omega), including the fi rst inverse moment, 1/lambda(B), from the expected high-statistics data of the BELLE II experiment.