While colloidal suspensions of nonspherical particles have been studied for decades, most work has focused on describing their behavior in flows with simple time behavior. Little is known about their behavior in flows with complex variations in time, and in particular, the possibility of varying the flow to control the suspension's properties. Here, we take advantage of a recent solution for the orientation dynamics of a dilute suspension under an arbitrary periodic, high-frequency shear flow to control particle alignment and suspension rheology. Working in the twin limit of rapid oscillations (Pe = 1/DTcyc >> 1, where D is the rotary diffusivity and T-cyc is the oscillation period) and long times t (Dt >> 1), we use a periodic simple shear waveform to strongly align particle orientations, aligning the orientations more strongly than steady shear by a factor proportional to the particle aspect ratio. Since particle orientations couple to the suspension stress, we can strongly control the rheology, maximizing and minimizing the viscosity and creating large normal stress signals. Surprisingly, the optimal waveforms are extremely simple, providing an intuitive understanding of the mechanisms for controlling particle alignment and suspension rheology. (C) 2017 The Society of Rheology.