Because of their excellent slice profiles and high immunity to RF inhomogeneity, adiabatic full passage (AFP) pulses are ideal for use in spatial localization. The nonlinear, position-dependent phase of a single AFP pulse generated during refocusing of transverse magnetization traditionally is eliminated by using identical pairs of AFP pulses, at the expense of increased RF power deposition and increased echo time (TE). Here it is shown that one can achieve significant phase refocusing by executing single AFP pulses along non-equivalent spatial axes. When used for volume selection in MR spectroscopic imaging (MRSI) the remaining nonlinear phase becomes inconsequential when the phase across a spectroscopic volume is small. Selection of rectangular and octagonal volumes is demonstrated with half the number of AFP pulses used in the traditional approach. It is shown that octagonal volume selection in the human brain provides excellent suppression of extracranial lipids, and thus allows multislice (1)H MRSI at 4 Tesla to be performed within the guidelines for RF power deposition.