Benchmark reaction barrier heights for the degenerate Cope rearrangements in the highly fluxional bullvalene and semibullvalene hydrocarbon cages are obtained at the CCSDT(Q) level close to the one-particle basis set limit and include inner-shell, scalar-relativistic, and Born-Oppenheimer corrections. Our best theoretical CCSDT(Q) Gibbs free reaction barrier height for semibullvalene (ΔG298‡ = 27.9 kJ mol-1) is in good agreement with the most recent experimental value of 25.9 kJ mol-1. However, our CCSDT(Q) reaction barrier height for bullvalene (ΔG298‡ = 62.2 kJ mol-1) indicates that the most recent gas-phase experimental value of 54.8 ± 0.8 should be revised upward.