Two modifications of the rho-axis-method torsion-rotation Hamiltonian for fitting spectra of methyl top molecules belonging to the C-s point group at equilibrium which are required to treat molecules with C-1 equilibrium configurations are described: (i) The permutation-inversion group must be changed from G(6) to G(3), which causes the A(1) and A(2) species to coalesce into a single A species, and which also introduces the slight complication of separably degenerate E species. (ii) One term must be added to the second-order contact-transformation-reduced Hamiltonian and seven terms must be added to the fourth-order reduced Hamiltonian. Programming strategies for this Hamiltonian are also discussed. In particular, portions of the C-1 computer code requiring complex arithmetic are indicated, and three schemes for checking the internal consistency of the C-1 code are suggested. Application of this C-1 Hamiltonian to ethylacetamidoacetate is given in the preceding paper. (C) 2003 American Institute of Physics.