A low molecular weight, slightly entangled polystyrene-polyisoprene (PS-PI) diblock copolymer is quenched from the disordered to a locally ordered but-macroscopically disordered lamellar state and then subjected to large-amplitude oscillatory shearing to induce a macroscopically aligned state. Substantial alignment is achieved; as shown by X-ray scattering; at high frequency and/or low temperature, the lamellae orient parallel to the shearing surfaces with their normal parallel to the velocity gradient, while at low frequency and/or high temperature, the normal to the lamellae orient perpendicular to both the shearing surfaces and the velocity gradient. These same two alignment directions were discovered earlier by Koppi et al; in shear-aligned polyolefin-polyolefin diblock copolymers, but in PS-PI, the alignment directions depend differently on temperature and frequency than in the polymers of Koppi et al. In our PS-PI, the alignment direction at each temperature and frequency Is that which as the lower value of the complex modulus G*; and the crossover from parallel to perpendicular alignment in our PS-PI sample occurs at a fixed value of the reduced frequency alpha(T) omega, where alpha(T) is the shift factor used to superimpose the linear moduli. The linear viscoelastic properties of the two different aligned states and their shift factors suggest that the parallel orientation is favored at high frequency for PS-PI because of the large contrast in the viscoelastic properties between the styrene and isoprene blocks.