Pile-up effects in radiation detectors are events in which two or more pulses overlap. In standard analog electronics pile-up events are rejected using a pile-up inspector. When digital acquisition techniques are used, the recorded waveforms of pile-ups can be elaborated and the contributing single pulses reconstructed. A method for the off-line digital processing of pile-ups from liquid organic scintillators (NE213) is proposed: pile-ups are reduced to single pulses and then correctly identified as neutrons (n) or gammas (γ). An analysis of the errors introduced by the method, depending on the number of fitted samples in the pulses, is given. The method has been applied to data acquired in the mixed n-γ field of JET deuterium plasma discharges from the NE213 detector in the central line of sight of the neutron profile monitor and the results are described.