Several theoretical and experimental aspects of sideband suppression in the nuclear magnetic resonance (NMR) spectra of rotating solids are considered. The principles of sideband suppression are explored using general symmetry arguments and previous treatments are examined critically. Analytical solutions are given for sideband suppression pulse sequences employing four, five, six, and nine pulses. The analytical solutions for four pulses are complete. Experimental demonstrations are given. The Journal of Chemical Physics is copyrighted by The American Institute of Physics. ; Several theoretical and experimental aspects of sideband suppression in the nuclear magnetic resonance (NMR) spectra of rotating solids are considered. The principles of sideband suppression are explored using general symmetry arguments and previous treatments are examined critically. Analytical solutions are given for sideband suppression pulse sequences employing four, five, six, and nine pulses. The analytical solutions for four pulses are complete. Experimental demonstrations are given. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.