Using a combination of electronic-structure methods, we have explored in some detail the regions of the C6H6 potential that are important for describing the recombination of propargyl (C3H3) radicals. Using this information in an RRKM-based master equation, we have been able to predict rate coefficients for a variety of elementary reactions, including the C3H3 + C3H3 recombination itself. Generally, the agreement between the theory and the limited amount of experimental information available is very good, although some discrepancies remain. The most important new feature of the present analysis (over our previous one) is the inclusion of a path on the potential that connects 1,2,4,5-hexatetraene to 1,3-hexadien-5-yne and then goes on to benzene and phenyl + H without passing through fulvene. The inclusion of this path in the analysis allows a number of experimental observations to be accounted for by the theory. From the results of the master equation calculations, we propose a simple, contracted model for describing the rate coefficient and product distribution of the C3H3 + C3H3 recombination reaction (and subsequent isomerizations) for use in flame modeling. Modified Arrhenius expressions are provided for the rate coefficients of the reactions appearing in the simplified model.