Experiences obtained from recent improvements in the performance of solid-state 14 N MAS NMR spectroscopy have been used in a natural abundance 33 S MAS NMR investigation of the satellite transitions for this interesting spin I=3/2 isotope. This study reports the first observation of manifolds of spinning sidebands for these transitions in 33 S MAS NMR as observed for the two alums XAl(SO 4 ) 2 ·12H 2 O with X=NH 4 and K. For the NH 4 -alum a variable temperature 33 S MAS NMR study, employing the satellite transitions, shows that the 33 S quadrupole coupling constant (C Q ) exhibits a linear temperature dependence (in the range −35°C to 70°C) with a temperature gradient of 3.1kHz/°C and undergoes a sign change with zero-crossing for C Q at 4°C (277K). For the isostructural K-alum a quite similar increase in the magnitude of C Q with increasing temperature is observed, and with a temperature gradient of 2.3kHz/°C. Finally, for optimization purposes, a study on the effect of the applied pulse widths at constant rf field strength on the intensity and variation in second-order quadrupolar lineshape for the central (1/2↔−1/2) transition of the K-alum has been performed.