The neutron capture width of the s-wave resonance at 34.8 keV in 27Al has been determined using a setup with extremely low neutron sensitivity. This feature is important because this resonance exhibits a very large scattering-to-capture ratio. 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 experiment. 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 data obtained with the individual detectors were corrected for the efficiency of the different converter materials. For that purpose, theoretical calculations of the capture gamma-ray spectra of the measured isotope and of gold, which was used as a standard, were performed. The final radiative width is gΓγ = 1.22 ± 0.07 eV. The accuracy is a factor of ∼3 better than in previous experiments.