The lowest-lying excited states of N-2 and CO are examined for the presence of intruder states that adversely influence the perturbative convergence in computations using multireference Moller-Plesset perturbation theory. Intruder states are found in the computations of the (3)Pi (u) state of N-2 and the (3)Pi state of CO. Since, in second order, these intruders-under normal circumstances-should make a negligible contribution to the target state, their contributions to the second-order energies are simply removed from the perturbation expansion. With the intruder state removed, the vertical excitation for the (3)Pi (u) ((3)Pi) state of N-2 (CO) is only 0.23 eV (0.35 eV) below the experimental value, compared to differing by 0.72 eV (0.44 eV) with the intruder state present. The intruder states are also removed by performing energy-denominator shifts using a redefined zeroth-order Hamiltonian H-0 that differs from previous treatments, since only the energy denominator associated with the intruder state is shifted. This approach removes intruders, but makes no other changes to the perturbation expansions. Two-state models are used to identify the intruder states and suggest remedies. (C) 2001 American Institute of Physics.