The one-step transformation of hydroxycyclohexadienyl radical into phenol by O-2 is modeled by the title hydrogen-abstraction reaction, which converts the simplest beta-hydroxy radical to an enol. The reaction is studied by different quantum-mechanical methods, to assess which level of theory is simultaneously reliable and affordable enough to investigate relatively large aromatic systems. Density functional theory (DFT(B3LYP)), unrestricted Moller-Plesset perturbation theory to the 2nd order (UMP2), and complete active space multiconfiguration self-consistent field (CAS-MCSCF) optimizations are first carried out to determine stable and transition structures. Then, more accurate energetics are determined by spin-projected single-reference PMP4//UMP2 calculations (which are compared with coupled cluster CCSD(T)//UMP2 results), and by two multireference second-order perturbation methods (MR-PT2), based on CAS-MCSCF wave functions and structures. With an (11,9) active space and the 6-311G(d,p) basis set, the MR-PT2 estimates for the energy barrier and reaction energy are: 14.5 and -12.1 kcal mol(-1) (CAS-PT2), and 8.3 and -13.4 kcal mol(-1) (MC-QDPT2). These estimates fall between the DFT(B3LYP)/6-311G(d,p) (3.3 and -19.1 kcal mol(-1)) and PMP4/6-311G(d,p) values (17.2 and -10.7 kcal mol(-1)). Single-point energy computations using larger basis sets are also discussed. The DFT(B3LYP) method tends to underestimate the barrier for H abstraction; the PMP4 barrier is likely to represent an upper bound, given that the single-reference perturbation expansion does not converge very efficiently. For extensions of the study to aromatics, DFT could be deemed to be an acceptable compromise between reliability and feasibility.