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Menus play an important role in both information presentation and system control. We explore the design space of shake menus, which are intended for use in tangible augmented reality. Shake menus are radial menus displayed centered on a physical object and activated by shaking that object. One important aspect of their design space is the coordinate system used to present menu options. We conducted a within-subjects user study to compare the speed and efficacy of several alternative methods for presenting shake menus in augmented reality (world-referenced, display-referenced, and object-referenced), along with a baseline technique (a linear menu on a clipboard). Our findings suggest tradeoffs amongst speed, efficacy, and flexibility of interaction, and point towards the possible advantages of hybrid approaches that compose together transformations in different coordinate systems. We close by describing qualitative feedback from use and present several illustrative applications of the technique.