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Mixed Reality provides a powerful medium for transparent and effective human-robot communication, especially for robots with significant physical limitations (e.g., those without arms). To enhance nonverbal capabilities for armless robots, this article presents two studies that explore two different categories of mixed reality deictic gestures for armless robots: a virtual arrow positioned over a target referent (a non-ego-sensitive allocentric gesture) and a virtual arm positioned over the gesturing robot (an ego-sensitive allocentric gesture). In Study 1, we explore the tradeoffs between these two types of gestures with respect to both objective performance and subjective social perceptions. Our results show fundamentally different task-oriented versus social benefits, with non-ego-sensitive allocentric gestures enabling faster reaction time and higher accuracy, but ego-sensitive gestures enabling higher perceived social presence, anthropomorphism, and likability. In Study 2, we refine our design recommendations by showing that in fact these different gestures should not be viewed as mutually exclusive alternatives, and that by using them together, robots can achieve both task-oriented and social benefits.