[en] Using the method of LIF we have measured with an average absolute error of 8% rate constants for rotationally inelastic collisions from level j/sub i/ = 8, 22, and 42 to level j/sub f/ = j/sub i/+Δj for Li(₂ (AΣ) colliding with Xe, Ar, and Ne. Values of Vertical BarΔjVertical Bar up to 32 were studied, involving rotational energy charges as large as 1.5 kT and collisions during which the Li₂ molecule rotated as much as 3 rad. These extremes are several times larger than the corresponding values in any previous experimental studies of rotationally inelastic collisions, and present a formidable challenge both to the experimental technique and to any general relationships used to fit the data. Four parameter fits with average deviation from the data of 11% have been found; these fits combine the energy corrected sudden approximation of DePristo et al. with our recently proposed power law-exponential expression for the basis rates k/sub j/→0