It is shown that the convergence of the configuration expansion of a many-electron wavefunction may be drastically improved without significantly complicating the energy matrix elements by using partially nonorthogonal orbitals. The wavefunction thus obtained is the many-electron analog to the natural orbital expansion of a two-electron wavefunction. The orbitals involved may be approximated by pseudonatural orbitals ("PNO-CI"), and an efficient way of calculating these orbitals is presented. An approximate treatment of multiple substitutions is discussed yielding a coupled electron pair theory formulated within the CI scheme. These methods are applied to the ground state and three ionized states of methane. Including only double substitutions, the computed upper bound to the energy of the ground state is -40.4584 hartree, i.e. 0.057 above the experimental nonrelativistic energy. About 83% of the total correlation energy is accounted for variationally, whereas the coupled-pair approximation yields 89%. The ratio between intraorbital and interorbital valence shell correlation energy is calculated as 1.56 in the case of localized electrons. The equilibrium distance in CH4 is found to be shifted from 2.046 bohr to 2.061 bohr due to correlation, and the harmonic frequency v\ is reduced from 3149 cm-1 to 3037 cm -1. These results indicate that the anharmonicity corrections to the observed values have probably been over estimated. The correlation contributions to the ionization potentials are analyzed. The theoretical potentials differ from the observed values by 1 %-2 %. The energy surface of CH4+ is investigated and is used to discuss the photoelectron spectrum of CH. Contrary to previous work, the lowest minimum of CHU+ is found to have Cv, symmetry. In all applications the variational results are compared with those of the independent-pair and coupled-pair approaches, and it is concluded that the latter represents a definite improvement over the first two.