In a vapour cell Li₂ molecules were excited by a CW argon-ion laser. Optical pumping depletes the population of the Li₂(x¹ Sigma _g⁺, nu "=1,J"=24) level. In the presence of foreign inert gases (He to Xe) collisional relaxation from the adjacent rotational levels takes place, which is measured by means of CW dye-laser-induced fluorescence. From the pressure dependence of the fluorescence signal, rate constants for mod Delta J mod =2,4,6 transitions in the ground state were obtained by solving the rate equations numerically. The values for mod Delta J mod =2 are of the order of 0.5-1.5*10^-10cm³s^-1, corresponding to effective cross sections of 5-10AA². Effective cross sections for total collision-induced vibrational transfer out of the nu "=1,J"=24 level were also obtained, which increase from 0.8AA² to 12.9AA² (from He to Xe).