Autocatalytic, lower-temperature (less than or equal to1100 K) methane pyrolysis has defied mechanistic explanation for almost three decades. The most recent attempt (by Dean in 1990) invoked the chemically activated addition of an allyl radical to acetylene, leading to a cyclopentadiene/cyclopentadienyl chain-branching system that prompted the observed autocatalysis. However, newer, more accurate thermochemical data for the cyclopentadienyl radical render that explanation untenable. A new model for methane pyrolysis is constructed here, using a novel mechanism generation approach that automatically computes any needed rate constants k(T,P) for chemically or thermally activated pressure-dependent reactions. The computer-generated mechanism accurately predicts the observed autocatalysis and concentration profiles without any adjustable parameters. Radical-forming reverse disproportionation reactions-which involve propyne, allene, and fulvene-account for at least half of the experimentally observed autocatalytic effect. Many of these reverse disproportionations were neglected in previous studies. The cyclopentadienyl radical is also important, but it is formed primarily by the chemically activated reaction of propargyl with acetylene. New rate estimates for unimolecular ring-closure reactions of unsaturated radicals are also presented. This approach is the first to incorporate pressure-dependent reactions generally and systematically during computerized mechanism construction. It successfully identifies complex but critical chemical-reaction pathways and autocatalytic loops missed by experienced kineticists.