Collisional energy transfer between 1-DELTA-g and 1-SIGMA-g+ Rydberg states of K2 has been studied by optical-optical double resonance (OODR) resolved fluorescence spectroscopy. The collision-induced probability for transition from a 1-DELTA-g state to an adjacent 1-SIGMA-g+ state of K2 depends much more strongly on DELTA-J than on DELTA-E in each case studied. DELTA-J = 0 collision transfer is more favorable than DELTA-J = +/- 2, ... for 1-DELTA-g odd Je levels. For 1-DELTA-g even Jf levels, DELTA-J = +/- 1 transfers are most favorable. The measurements of intensities of 1-DELTA-g, 1-SIGMA-g+ <-- B 1-PI-u, v' = 2, J' = 14e transitions and fluorescence intensities show that the collision-induced transition probability of these 1-DELTA-g - 1-SIGMA-g+ systems is quite large.