Three multiple-pulse spin-echo experiments that have been used to enhance the sensitivity of broad powder patterns obtained from NMR spectra of spin-1/2 and half-integer quadrupolar nuclei in polycrystalline solids are examined. Specifically, the Carr-Purcell Meiboom-Gill (CPMG), the Mansfield-Waugh (MW-4), and a modified version of the CPMG experiment (modified-CPMG) are described and compared. Use of these pulse sequences results in transforming the broad powder lineshapes into a series of narrow spikelets whose overall envelope mimics that obtained from the normal Hahn-echo experiment. The CPMG and modified-CPMG methods can result in a considerable saving in experiment time and are particularly powerful in studying the central transition of halfinteger spin quadrupolar nuclei. Artifacts generated by the MW-4 sequence or caused by imperfections in the pulses in the CPMG sequences are explained using a product operator analysis.