The factors affecting kinetic isotope effects in barrierless recombination reactions are considered from the perspective of variational transition state theory (VTST). Despite the broad application of VTST methods, a general consideration of kinetic isotope effect predictions of the theory has not previously been undertaken, especially for cases where changes in the internal structure and vibrational frequencies of the fragments (i.e., the conserved modes) can be assumed to be negligible. Use of the center-of-mass separation as the reaction coordinate in such a case entails some restriction on the range of kinetic isotope effects which can be accommodated. Larger effects are possible within a variable reaction coordinate implementation of transition state theory, and the predicted kinetic isotope effects are shown to be strongly dependent on the location of the pivot point. Illustrative model calculations demonstrate the feasibility of reproducing the experimentally observed kinetic isotope effects for the CH + O-2, HCC + O-2, CH + C2H2, and CH + C2H4 reactions with realistic deviations of the pivot points from the center-of-mass. In contrast, calculations restricted to center-of-mass pivot points predict isotope effects that are even inverted. For the CH + CH4 reaction, the isotope effects appear too large to be explained by the reaction coordinate variations, and changes in the conserved modes play a key role in the observed isotope effects, as demonstrated with ab initio based TST simulations. Overall, the experimentally observed kinetic isotope effects in CH addition reactions are strongly suggestive of an optimum reaction coordinate corresponding to a pivot paint located near the center of the radical orbital.