We have examined the changes in rotation that occur simultaneously with a change in vibrational state within a large polyatomic. Specifically, a variety of rotational-level population distributions have been prepared in the 6(1) vibrational level of B-1(2u) benzene, and the rotational distributions within 0(0) that result from collisions with H-2, D-2, or CH4 have been observed by measuring the rotational contour of the 6(1)(0) band in emission. The experiments were performed in the collision region of a supersonic free jet expansion at a translational temperature of 34 K (H-2 and D-2) or 18 K (CH4). It is demonstrated that rotational-energy transfer within 6(1) and 0(0) does not obscure the rotational changes accompanying the vibrational change. For a particular collision partner, the final rotational distributions in 0(0) are essentially the same for all initial 6(1) distributions. However, the final 0(0) rotational distributions are quite different for the different collision partners. The observed 6(1)(0) rotational contours are fit reasonably well by a thermal distribution with 0(0) rotational temperatures of 19, 41 and 93 K for H-2, D-2, and CH4, respectively. The 6(1)(0) rotational contours were also fit using an exponentially decaying momentum gap model to evolve the initial 6(1)(0) rotational distribution to the final 0(0) distribution. As an illustration, for an initial J, K distribution with average J and K values of 8 and 6, respectively, the changes in these average values are (written as (Delta(J) over bar, Delta(K) over bar)) (3, 1), (8, 4), and (16, 9) for the thermal distribution fits for H-2, D-2, and CH4, respectively. The corresponding values for the momentum gap model are (4, 0), (10, 1), and (19, 8). The modeling shows that the \DeltaK\ changes are much larger for CH4 than for H-2 and D-2. A possible reason for the relaxed DeltaK restriction with CH4 May be that a broad range of collision geometries leads to 6(1) --> 0(0) vibrational-energy transfer with this partner. The 0(0) distributions for D-2 are broader than for H-2, illustrating that the reduced mass and rotational-level spacings play an important role in determining the rotational changes that occur.