Organic NE213 liquid scintillator neutron detectors are commonly used at accelerator facilities for neutron beam diagnostics. In recent years, they have also been installed at nuclear fusion facilities to measure the neutron energy spectra from Deuterium (D) and Deuterium-Tritium plasmas, e.g., at the ASDEX Upgrade (Garching, Germany) and at the Joint European Torus (JET, Culham, UK). The NE213 equivalent scintillating material (now BC501A) of the detector is sensitive to neutron and gamma radiation, so pulse discrimination techniques are applied in order to obtain the measured neutron pulse height spectrum (PHS). If the neutron detector is stable, controlled, and well-characterized (i.e., its response function to incoming neutrons of known energy is determined with high accuracy), it can be used as a neutron spectrometer. The measured PHS can then be analyzed using standard techniques such as unfolding to determine the incoming neutron energy spectrum. This article focuses on the unfolding of neutron data measured in D plasma experiments at JET by a compact broadband neutron spectrometer using the maximum entropy unfolding code MAXED. A general method for optimizing MAXED input parameters is described and applied to the measured PHS to diagnose the effects of the auxiliary heating of JET D plasma on the neutron energy spectra.