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Energy consumption of portable RFID readers is becoming an important issue as applications of RFID systems pervade many aspects of our lives. Surprisingly, however, these systems are not energy-aware with the focus till date being on reducing the time to read all tags by the reader. In this work, we consider the problem of tag arbitration in RFID systems with the aim of designing energy-aware anticollision protocols. We explore the effectiveness of using multiple time slots per node of a binary search tree through three anticollision protocols. We further develop an analytical framework to predict the performance of our protocols and enable protocol parameter selection. We demonstrate that all three protocols provide significant energy savings both at the reader and tags (if they are active tags) compared to the existing Query Tree protocol, while sharing the deterministic property of the latter. Further, we show that our protocols provide similar benefits even with correlated tag IDs.