The inclusive and fiducial t¯t production crosssections are measured in the lepton+jets channel using 20.2 fb−1 of proton–proton collision data at a centre-of-mass energy of 8 TeV recorded with the ATLAS detector at the LHC. Major systematic uncertainties due to the modelling of the jet energy scale and b-tagging efficiency are constrained by separating selected events into three disjoint regions. In order to reduce systematic uncertainties in the most important background, the W+jets process is modelled using Z+jets events in a data-driven approach. The inclusive t¯t cross-section is measured with a precision of 5.7% to be σinc(t¯t) = 248.3±0.7 (stat.)±13.4 (syst.)±4.7 (lumi.) pb, assuming a top-quark mass of 172.5 GeV. The result is in agreement with the Standard Model prediction. The crosssection is also measured in a phase space close to that of the selected data. The fiducial cross-section is σfid(t¯t) = 48.8±0.1 (stat.)±2.0 (syst.)±0.9 (lumi.) pb with a precision of 4.5%.