The threshold photoelectron spectra for the lowest vibrational levels of the CO+ A (II)-I-2 state are presented and discussed. These spectra were recorded with single-photon excitation of jet-cooled CO molecules, using pulsed field ionization to detect the ionization thresholds with rotational resolution. One of the sub-bands, corresponding to the A (II1/2)-I-2 (nu(+) = 0) level, is perturbed by the X (2) Sigma(+) (nu(+) = 10) level, and the spectrum appears quite different from the corresponding nu(+) = 1 band. An explanation based on core relaxation induced by Rydberg electron-ion core collisions is invoked to explain the observed spectrum. For the other unperturbed bands, a simulation based on a standard model for rotational line strengths in photoelectron spectra provides a satisfactory description of the spectra. The results of this simple model are compared with detailed ab initio calculations.