Partially deuterated methyl groups in single crystals of aspirin are investigated by deuteron NMR at temperatures between 8 K and room temperature. The CH2D groups perform reorientations which are governed by a rotational potential with three wells, two of which are almost equally deep whereas the third is significantly deeper. At temperatures below 20 K, a so far unobserved type of incoherent tunneling process is identified. This process consists in reorientations between the two upper potential wells which are fast on the time scale of the quadrupolar interaction, whereas transitions into the deeper well are slow on this time scale. At temperatures above 35 K, the methyl groups perform thermally activated stochastic reorientations between all three potential wells. By determining the relative populations of the three wells as a function of temperature, the energy difference between the lower and the two upper wells is found to be 3.3 meV. This amounts to almost 8% of the average barrier height, which is determined from the temperature dependence of the spin-lattice relaxation time to be 43 meV.