We present a sequence of three successively improved new semiempirical potential energy surfaces for the reaction CH3 + H 2→CH4+H. The semiempirical calibration is based on ab initio electronic structure calculations and experimental thermochemical data, vibrational frequencies, reaction rate constants, Arrhenius parameters, and kinetic isotope effects (KIE's). To compare to the experimental kinetic data we apply variational transition state theory and semiclassical estimates of tunneling probabilities. We also provide detailed factorization analyses of the KIE's to illustrate the way in which various surface features contribute to the overall KIE's, and we discuss the substantial difficulties in attributing specific kinetic results to isolated potential energy surface features. Each of the three new surfaces, called J 1, J 2, and J 3, has a thinner barrier than the one before. In addition, we provide one example, called surface J 2A, showing the effect of making the barrier even thinner than on the best surface. The best surface yields rate constants for the forward and reverse reaction, activation energies, and KIE's that are consistent with most of the available experimental data.