Following work by Slater and Bunker, the unimolecular rate constant versus collision frequency, kuni(ω,E), is expressed as a convolution of unimolecular lifetime and collisional deactivation probabilities. This allows incorporation of nonexponential, intrinsically non-RRKM, populations of dissociating molecules versus time, N(t)/N(0), in the expression for kuni(ω,E). Previous work using this approach is reviewed. In the work presented here, the biexponential f1exp(-k1t) + f2exp(-k2t) is used to represent N(t)/N(0), where f1k1 + f2k2 equals the RRKM rate constant k(E) and f1 + f2 = 1. With these two constraints, there are two adjustable parameters in the biexponential N(t)/N(0) to represent intrinsic non-RRKM dynamics. The rate constant k1 is larger than k(E) and k2 is smaller. This biexponential gives kuni(ω,E) rate constants that are lower than the RRKM prediction, except at the high and low pressure limits. The deviation from the RRKM prediction increases as f1 is made smaller and k1 made larger. Of considerable interest is the finding that, if the collision frequency ω for the RRKM plot of kuni(ω,E) versus ω is multiplied by an energy transfer efficiency factor βc, the RRKM kuni(ω,E) versus ω plot may be scaled to match those for the intrinsic non-RRKM, biexponential N(t)/N(0), plots. This analysis identifies the importance of determining accurate collisional intermolecular energy transfer (IET) efficiencies.