The Rydberg states L1PI (v = 0), L'1PI (v = 1), K1SIGMA+ (v = 0), W1PI (v = 0), and W'1PI (v = 2) have been studied in a 2 + 1 double-resonance detection scheme with a resolution of 0.005 cm-1. Accurate molecular constants have been derived for these states. From the observed linewidths of individual rotational transitions, predissociation rates for the Rydberg states have been deduced. For the first time a clear J and e/f dependence for the predissociation of CO has been observed. One of the states causing the observed predissociation could be identified as the D'1SIGMA+ state.