Abstract It is shown that the confinement of electrons in narrow conducting channels, modelled with a parabolic well, leads to asymmetric quantized Hall plateaus about complete Landau-level fillings and to saw-toothed oscillations in the resistivity ϱ xx as a function of the magnetic field B. The peaks in ϱ xx are shifted to lower B and drastically reduced from their wide-channel values, as observed by Zheng et al. . The corrections to the quantized Hall conductivity resulting from the finite width of the samples, are evaluated. Further corrections due to the finite thickness of the samples and the response to finite frequencies are taken into account.