Two modified MREV8 sub-cycles forming a partially pertially permuted cycle (PP16) have been used in a multipulse study of the mesophases formed by the lithium perfluoro-octanoate (LiPFO)+ water system. The lineshapes show characteristic axially symmetric chemical shift tensors which have been measured over a range of temperature (20-68°C) and concentration (47.8-72% LiPFO).The shift anisotropy in the hexagonal phase is halved in magnitude and opposite in sign to that observed in the lamellar phase, indicating the presence of rapid rotational diffusion. A rotational study of an aligned hexagonal sample (47.8 % LiPFO:52.2 % H2O) is used to demonstrate the effects of two dimensional averaging on a chemical shift tensor.The observed shift tensors are used to estimate values for the order parameter based on the known values of the ¹⁹F chemical shift tensor elements for CF2 groups in Teflon at liquid nitrogen temperatures. When compared with chain dimensions estimated from X-ray data, the values of S indicate the existence of rotational isomerisation for the surfactant chain. The molecular order generally increases with increasing concentration, but a decrease is observed at the hexagonal/lamellar boundary.