An optical-optical double resonance procedure is used to compare the relative populations of e/f spin components of the X2-SIGMA-g+(upsilon = 7) rotational manifold resulting from the collision-induced electronic transitions in N2+ for the cases of large and small energy gaps. Rotational levels of the A 2II(ui)(upsilon = 3 or 4) vibrational state of N2+ are selectively populated with a pump laser. Transitions to rotational levels of the X2-SIGMA-g+(upsilon = 7) level due to collisions with bath gas helium atoms at room temperature are monitored by scanning the lines of the B-X(5,7) band with a second, probe laser. The relaxation pathways A(upsilon = 3) --> X (upsilon = 7) and A(upsilon = 4) --> X (upsilon = 7) traverse energy gaps (DELTA-E) of approximately 0 and approximately 1760 cm-1, respectively. Perturbations of the rotational levels of the B2-SIGMA-u+(upsilon = 5) state by the A 2II(u1/2)(upsilon = 17) manifold allows for the e/f, spin-rotation splitting of the lines of B-X(5,7) probe laser scan to be resolved. The effects of these perturbations on the relative intensities of the B-X(5,7) lines have been taken into account. The intensity patterns for collision-induced transitions across the two widely different energy gaps are nearly identical, indicating that the propensities for this case have an insignificant energy-gap dependence. These detailed propensities from selectively excited rotational levels of the A(upsilon = 4 or 3) level to the individual, nearly degenerate rotational levels of the X(upsilon = 7) manifold are compared with theoretical models for inelastic scattering between 2-PI and 2-SIGMA electronic states.