The neutron capture widths of s-wave resonances in 56Fe (27.7 keV), 58Ni (15.4 keV), and 60Ni (12.5 keV) have been determined using a setup completely different from previous experiments. A pulsed 3-MV Van de Graaff accelerator and a kinematically collimated neutron beam, produced via the 7Li(p, n) reaction, were used in the experiments. Capture gamma rays were observed by three Moxon-Rae detectors with graphite, bismuth-graphite, and bismuth converters, respectively. The samples were positioned at a neutron flight path of only 9 cm. Thus, events due to capture of resonance-scattered neutrons in the detectors or in surrounding materials are completely discriminated by their additional time of flight. The high neutron flux at the sample position allowed the use of very thin samples (0.15 to 0.45 mm), avoiding large multiple scattering corrections. The data obtained with the individual detectors were corrected for the efficiency of the respective converter materials. For that purpose, detailed theoretical calculations of the capture gamma-ray spectra of the measured isotopes and of gold, which was used as a standard, were performed. The final results are Γγ(27.7 keV, 56Fe) = 1.06 ± 0.05 eV; Γγ(15.4 keV, 58Ni) = 1.53 ± 0.10 eV; and Γγ(12.5 keV, 60Ni) = 2.92 ± 0.19 eV. The accuracy obtained with the present experimental method represents an improvement by a factor 3 to 6 compared to previous experiments. The investigated s-wave resonances contribute 10 to 40% to the total capture rate of the respective isotopes in a typical fast reactor.