Moderate-size basis set ab initio calculations for the pi-electron vertical ionization potentials of trans- and cyclobutadiene (116 and 128 functions, respectively) are performed using the effective valence shell Hamiltonian (H(nu)) method. These calculations demonstrate the flexibility and unique features of the H(nu) method because the ionization potentials emerge from previous computations of the neutral valence-like and Rydberg state excitation energies using the same H(nu). The computed ionization potentials agree well with experiment and with previous calculations, including highly correlated ones for trans-butadiene. New predictions are provided for ionizations to quartet and shake-up states. Furthermore, in contrast to current beliefs about quasidegenerate perturbation theory, the third-order H(nu) calculations do not encounter intruder state problems.