In this paper we have carried out a test of current multilevel electronic structure methods to give accurate rate constants for the reactions CHnD4-n+OH-->P and for the reaction of methane with OD. These multilevel methods are single-point energy techniques designed as general parametrizations for extrapolation to the full configuration interaction limit and, in some cases, to attain also the infinite basis set limit. By means of variational transition state theory including multidimensional tunneling corrections, the rate constants for these reactions, over a wide range of temperatures, have been computed using two recently developed multicoefficient schemes for extrapolating correlated electronic structure calculations: multicoefficient scaling all correlation (MCSAC) and multicoefficient correlation methods (MCCM). For comparison purposes, we have also evaluated the same rate constants using two other multilevel extrapolation techniques, namely, the multicoefficient quadratic configuration interaction (MC-QCISD) method and the complete basis set extrapolation model for free radicals (CBS-RAD). Two dual-level direct dynamics techniques have been employed within the scheme of variational transition state theory: the interpolated single-point energy corrections (ISPE) and the interpolated optimized corrections (IOC), with the purpose to analyze the importance of correcting a low level potential energy surface with the optimizations of the stationary points carried out at the highest computational level affordable. We have shown that the so-called MCCM-CCSD(T)-1sc multilevel scheme provides the best results for the set of reactions studied. A slight difference from the experimental rate constants still persists, specially at the lowest temperatures, although we think that the best theoretical rate constants of the present paper are accurate enough for most of the practical applications. However, the kinetic isotope effects (KIEs) are not so well reproduced because the deviations of the individual theoretical rate constants from the experimental ones, although being very small, do not go in the same direction and these errors are reinforced when the corresponding KIE is calculated.