Novel methods to analyze NMR signals dominated by dipolar interaction are applied to the study of slow relaxation motions in polybutadiene approaching its glass transition temperature. The analysis is based on a recently developed model where the time dependence in an ensemble of dipolar interacting spin pairs is described without resorting to the Anderson-Weiss approximation. The ability to catch relevant features of the relaxation process is emphasized. In particular, it is shown that the temperature profile of the Magic Sandwich Echo efficiency carries information on the frequency profile of the -process. The analysis is corroborated by the temperature dependence of the spin-lattice relaxation time.