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This report presents techniques for using discrete finite rotations to reorient a spacecraft from a given initial attitude to a final attitude which satisfies a specified aiming objective. The objective may be a fully specified final orientation or it may require that the spacecraft direct an instrument along a certain direction. Constraints are also imposed on the allowable intermediate orientations that the spacecraft may assume during the course of the maneuver, representing the operational requirements of onboard instrumentation. The algorithms presented consider solutions that will achieve the desired objective with only one or two slew maneuvers, although they may be easily extended to consider more complicated solutions requiring additional maneuvers.