Members of the np\sigma 3\Sigma+ (v=0) Rydberg series of the CO molecule in the range n = 5--8 have been detected and rotationally analysed using a three-step excitation scheme via a perturbed valence "doorway" state. Starting from n=6, l-uncoupling becomes evident. Molecular constants for a p-complex Hamiltonian have been obtained. Strong predissociation, growing with n, was found for all observed members of the series. The N-dependence of the line widths is explained by the combined effects of l-uncoupling and a homogeneous perturbation of the np pi 3Sigma+ states.