Vibrational Herzberg bands of the O-2 molecule just below its first O(P-3)+O(P-3) dissociation limit are since long-known to be perturbed. Jenouvrier [J. Mol. Spectrosc. 198, 136 (1999)] assigned the cause of the perturbations to five vibrational levels supported by the shallow minimum in the 1 (3)Pi(u) potential energy curve around 5.5a(0). 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 (3)Pi(u) multiplet was not correct. Based on our calculation we present a new assignment of the perturbing states: 1 (3)Pi(u,Omega=2)(v=0), 1 (3)Pi(u,1)(0), 1 (3)Pi(u,2)(1), 1 (3)Pi(u,1)(1), and 1 (3)Pi(u,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.