Rates for rotational relaxation within the 61 vibrational level of S1 (1B2u) benzene have been measured in a gas cell at room temperature for the collision partners He, H2, Ar, N2, cyclohexane, and S0 benzene. The relaxation rates are large and are in excess of the hard-sphere elastic collision rate for all collision partners. The efficiencies for rotational relaxation, defined as the observed rate constant normalized to the hard-sphere collision rate constant, show H2 to be of similar efficiency to helium; however, N2 was found to be significantly more efficient than Ar. Cyclohexane was found to be relatively inefficient. The general trend in relaxation rates is reflected more accurately by the Lennard-Jones (LJ) elastic collision rate than by the hard-sphere rate, but even in this case the efficiencies for the gases studied generally exceed this rate, suggesting that the attractive potential involved is more long range than the LJ potential.