Multiple-quantum magic-angle-spinning (MQMAS) NMR experiments have recently been used to remove second-order broadening from the central transition of half-integer quadrupolar nuclei. In this paper, the various methods that have been proposed for obtaining pure absorption-mode Lineshapes in MQMAS experiments are described and compared. The methods can be classified according to whether the data are amplitude-or phase-modulated as a function of the evolution period, t(1). Both classes of experiment are usually performed in such a way that the inhomogeneous quadrupolar broadening is spread out along a ridge which, for spins I = 3/2 and 5/2, respectively, has a slope of -7/9 or 19/12 with respect to the F-2 axis. This paper shows, however, that there are disadvantages associated with recording the data in this fashion and demonstrates, in particular, that a shearing transformation of the final two-dimensional spectrum can lead to distorted Lineshapes. Novel amplitude-and phase-modulated ''split-t(1)'' MQMAS experiments are introduced which fully refocus the second-order broadening during the evolution period, t(1), thereby avoiding the need for a shearing transformation. The considerable practical advantages of these split-t(1) experiments are discussed, particularly with regard to ease of implementation and processing. In general, the sensitivities achievable using the split-t(1) MQMAS experiments are predicted to be similar to those obtainable with other methods and, in the special case of the spin I = 3/2 phase-modulated experiments, are even shown to be slightly superior. (C) 1997 Academic Press.