The proton-coupled, carbon-13 "magic-angle" sample-spinning nuclear magnetic resonance spin-lattice relaxation behavior of poly (cis-isoprene) and poly (cis-butadiene) as a function of temperature is reported. Analysis of the relaxation behavior of the methine carbons reveals strong temporal correlations between the 13CH dipolar and 13C anisotropic chemical shielding interactions. Equations are presented which enable the interpretation of these interferences for non-axially symmetric shielding tensors, subject to cylindrically symmetric reorientation. In the context of these expressions, the results indicate that the methine moiety in each of the two polymers executes relatively rapid, isotropic motions, on the time scale of the carbon-13 Larmor frequency. It is also shown that in certain polymeric systems, the sign of the interference term may change with frequency. This intriguing property provides additional insight into the relative reorientational anisotropies of the low- and high-frequency motions, and the specific case of the spin-lattice relaxation and differential line broadening of the methine carbons in poly (cis-isoprene) and poly (trans-isoprene) is considered in detail.