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In a multi-user augmented reality application for a shared physical environment, it is possible for users to interfere with each other. For example, in a multi-player game in which each player holds a display whose tracked position and orientation affect the outcome, one player may physically block another player's view or physically contact another player. We explore software techniques intended to avoid such interference. These techniques modify what a user sees or hears, and what interaction capabilities they have, when their display gets too close to another user's display. We present Redirected Motion, an effective, yet nondistracting, interference avoidance technique for hand-held AR, which transforms the 3D space in which the user moves their display, to direct the display away from other displays. We conducted a within-subject, formal user study to evaluate the effectiveness and distraction level of Redirected Motion compared to other interference avoidance techniques. The study is based on an instrumented, two-player, first-person-shooter, augmented reality game, in which each player holds a 6DOF-tracked ultra-mobile computer. Comparison conditions include an unmanipulated control condition and three other software techniques for avoiding interference: dimming the display, playing disturbing sounds, and disabling interaction capabilities. Subjective evaluation indicates that Redirected Motion was unnoticeable, and quantitative analysis shows that the mean distance between users during Redirected Motion was significantly larger than for the comparison conditions.