Terrestrial gamma-ray flashes (TGFs) are energetic photon bursts observed from satellites and associated with lightning activity. Comparison between calculations based on the model of relativistic runaway electron avalanches (RREA) in large-scale weak electric field in thunderstorms and satellite measurements usually shows that the photon spectrum is consistent with source altitudes around 15 km. However, recent observations have located intra-cloud lightning (IC) discharges responsible for TGFs much deeper in the atmosphere (at altitudes ∼10 km). In the present work, we show that the TGF spectrum as produced by acceleration of electrons in the strong electric field of stepping IC leaders is consistent with the lower altitudes recently discovered. This study reconciles observations and measurements by setting new altitudes for the TGF sources based on mechanism of direct acceleration of electrons in the lightning leader field. Moreover, the photon source beaming geometry is consistently determined from the geometry of electric field lines produced by the lightning leader.