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Neutron time-of-flight (nToF) signals from current-mode neutron detectors are often used to determine burn-averaged ion temperature from ICF targets because the spread of the neutron energy distribution is a function of the temperature of the reacting ions. The measured signal will, however, be a convolution of the actual neutron signal, the detector response, and the response of the recording system. In addition, scattered neutrons will arrive at the detector later than unscattered neutrons, further broadening the signal. The ion temperature derived from nToF data depends strongly on the functions used to fit the data or the methods utilized to unfold the neutron energy spectrum. A functional form based on known and measured properties of the detectors is used to fit the integral of the time-of-flight signal, allowing ion temperature derivations from targets with lower neutron yield than previously possible.