A composite theoretical method for accurate thermochemical kinetics, G3X-K, is described. This method is accurate to around 0.5 kcal mol(-1) for barrier heights and 0.8 kcal mol(-1) for enthalpies of formation. G3X-K is a modification of G3SX theory using the M06-2X density functional for structures and zero-point energies and parameterized for a test set of 223 heats of formation and 23 barrier heights. A reduced perturbation-order variant, G3X(MP3)-K, is also developed, providing around 0.7 kcal mol(-1) accuracy for barrier heights and 0.9 kcal mol(-1) accuracy for enthalpies, at reduced computational cost. Some opportunities to further improve Gn composite methods are identified and briefly discussed. (C) 2012 Elsevier B.V. All rights reserved.