The huge amount of optical photons emitted in burst by Cerium doped Lanthanum bromide scintillators poses a severe constraint on the specifications of photomultipliers, namely they must operate at very large instantaneous current values with minimum saturation of output pulse signals. Acquisition in shape and processing of photomultipliers output pulses by means of high-speed free-running analog to digital converters and processing devices allows specific correction for pulse saturation and distortion effects, due to high-gain tubes operated at relatively high power supply voltage. We analyze the effects of output signal saturation in photomultiplier tubes as a function of the high voltage level and the amount of energy released in the scintillator crystal, proposing a simple model to characterize this complex phenomenon. According to the proposed model, a preliminary first-order correction is calculated and applied to the energy estimations obtained by a traditional analog spectroscopy system, for energies up to 9 MeV, reducing the maximum estimation error by almost an order of magnitude.