We have measured the temperature and Larmor frequency dependence of the proton spin-lattice and spin-spin relaxation rates in solid isopropylbenzene. The sample melts at too low a temperature to observe the high-temperature frequency-independent regime from which a rotational barrier is normally extracted. By measuring the rates at three Larmor frequencies, however, we demonstrate that all the relevant parameters that characterize methyl reorientation can be overdetermined within the confines of a given dynamical model even though the model may not be unique. The relaxation technique is very sensitive to the state of the solid, and interesting and unusual thermal history effects are presented and discussed.