We have extended and improved previous calculations of cross-sections for the rotational excitation by helium of A- and E-type methanol in their torsional ground states. We increased the maximum value of the rotational quantum number, j, of the methanol molecule from j= 9, used in the previous calculations, to j= 15, thereby ensuring the completeness of the rotational energy levels and the corresponding basis of eigenfunctions up to the first threshold for exciting the internal torsional motion of the molecule. The representation of the rotational–torsional eigenfunctions of E-type methanol has been improved significantly. We compare the results of the present calculations, which were performed in both the coupled channels (CC) and the coupled states (CS) approximations, with the previous results. All the calculations exhibit the same collisional propensities, but there exist quantitative discrepancies, for individual transitions, between both the present and previous determinations and also between the present CC and CS results, notably for E-type methanol. Cross-sections have been generated on an energy grid that is adapted to the evaluation of the thermal rate coefficients at low temperatures (10 ≤T≤ 200 K); these data are available online.