The lowest-lying excited states of N2 and CO are examined for the presence of intruder states that adversely influence the perturbative convergence in computations using multireference Møller-Plesset perturbation theory. Intruder states are found in the computations of the 3Πu state of N2 and the 3Π 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 3Πu (3Π) state of N2 (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 H0 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.