The laboratory millimeter- and submillimeter-wave spectrum of the symmetric (A) and degenerate (E) substates of 12CH3OH has been extended to include 437 transitions through J ≤ 10 and K ≤ 8 in the first three torsional states (vt = 0,1,2) of the A species and 419 transitions through rotational quantum numbers J ≤ 10, |K| ≤ 8 in the vt = 0 torsional state, and |K| ≤ 6 in the vt = 1,2 torsional states of the E species. Modification of the extended internal axis method (IAM) Hamiltonian to include more cross terms which describe the interaction of rotation and torsion as well as the separation of the fits of the A and the E species have reduced the overall root-mean-square deviation to the level of the experimental uncertainty. This makes possible a very significant improvement in the calculation of the rotational-torsional spectrum of methanol in this spectral region. The spectral constants generated by the fit have been used to predict an additional 569 lines of 12CH3OH for Vt = 0,1,2 and rotational quantum number J ≤ 12.