Multichannel pulse height measurements with a cylindrical ³He proportional counter obtained at a reactor filter of natural iron are taken to investigate the properties of three algorithms for neutron spectrum unfolding. For a systematic application of uncertainty propagation the covariance matrix of previously determined ³He response functions is evaluated. The calculated filter transmission function together with a covariance matrix estimated from cross-section uncertainties of the filter material is used as fluence pre-information. The results obtained from algorithms with and without pre-information differ in shape and uncertainties for single group fluence values, but there is sufficient agreement when evaluating integrals over neutron energy intervals.