Resonance cross sections relevant for the termination of the s-process reaction path have beendetermined for 204,206,207Pb and 209Bi at the CERN neutron time-of-flight spectrometer n_TOF.Themeasurementswere carried out in the neutron energy range from1 eV up to 500 keV. By usinga system of C6D6-detectors with optimized neutron sensitivity, the main corrections of previousmeasurements related to backgrounds from scattered neutrons could be practically eliminated.Other corrections were thoroughly treated by control measurements with additional samples fordetermination of the ambient background and of background from in-beam g -rays as well as bydetailed analyses via Monte Carlo simulations. The Maxwellian averaged cross sections of thefour isotopes and their implications for the s-process abundance contributions in the Pb/Bi regionare discussed.