Small angle neutron scattering was used to investigate the orientational ordering of a lyotropic mixture of cesium-perfluoro-octanoate (CsPFO) in water under simple Couette and oscillatory shear. The discotic-liquid-crytstal micelles were found to orient mostly parallel to the moving shear cell walls (i.e., vertically). A partial ‘‘flipping’’ of the orientation was observed in the smectic phase, whereby lamellae were seen to orient horizontally. Oscillatory shear produced orientational effects as well as shear-induced shifts of the phase transition boundaries. Interesting competing ‘‘bulk’’ and ‘‘wall’’ effects were also observed.