Broadening factors were obtained analytically and computationally for three models of thermal unimolecular reactions. All three models incorporate weak collision effects. In two of the models the exponential formula was assumed for the energy transfer. The Lindemann formula was assumed for the microcanonical rate constants in one of the models, the extended Kassel formula in the other. In the third model the extended Kassel formula was assumed for the microcanonical rate constants, and the stepladder formula was assumed for the energy transfer. The broadening factor F was expressed as a function of u, a bounded variable obtained from an algebraic transformation of the collision frequency. As a function of u(m) F has a single minimum. Weak collisions were found to shift the location of this minimum, call it u(m), in the negative direction, but the shifts are small for the extended Kassel models. Weak collisions have more of an effect on F(u(m)), causing it to decrease. In no case, however, was F(u(m)) found to decrease by more than 0.25. The decrease in F(u(m)) as a function of average energy transferred per collision was found to be approximately the same for all three models.