We present the first measurements of ion rotational distributions for photoionization over an extended range [0 less than or equal to E(K) less than or equal to 200 eV for N-2 (2 sigma(u)(-1)) and 3 less than or equal to E(K) less than or equal to 125 eV for CO (4 sigma(-1))]. The N-2 ion rotational distributions are seen to change dramatically over this energy range, indicating that characteristically molecular behavior of the photoelectron persists far from ionization threshold. In addition, the N-2 and CO results show a strikingly different dependence on energy. Although differences are expected due to the absence of a center of symmetry in CO, detailed calculations reveal that this behavior arises from the presence of Cooper minima in the 2 sigma(u)-->k sigma(g) continuum in the case of N-2 and from an f-wave shape resonance in the 4 sigma-->k sigma channel in CO. Agreement between measured and calculated ion rotational distributions is excellent. The N-2 results are also compared with electron bombardment ionization data. This comparison demonstrates that previous interpretations of electron bombardment data are prone to errors.