Vibrational Herzberg bands of the O2 molecule just below its first O3P+O3P dissociation limit are since long-known to be perturbed. Jenouvrier [et al.] [J. Mol. Spectrosc. 198, 136 (1999)] assigned the cause of the perturbations to five vibrational levels supported by the shallow minimum in the 1 3Piu potential energy curve around 5.5a0. Using ab initio potential energy curves and spin-orbit couplings from previous work [J. Chem. Phys. 116, 1954 (2002)] we present a full quantum calculation of all ungerade rotation-vibration-electronic states of oxygen just below the dissociation threshold, through a total angular momentum quantum number of J=19. This calculation shows that the original assignment, based on a Hund's case (a) model of a regular 1 3Piu multiplet was not correct. Based on our calculation we present a new assignment of the perturbing states: 1 3Piu,[Omega=2) (v=0, 1 3Piu,1)(0, 1 3Piu,2) (1, 1 3Piu,1)(1, and 1 3Piu,0-)(0 in order of ascending term values. We show the new assignment to be consistent with experimental data and we also propose new spectroscopic parameters for the perturbing states.