Energy consumption of mobile readers is becoming an important issue as applications of RFID systems pervade different 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. The problem of tag arbitration in RFID systems is considered with the aim of trading off time for energy savings at the reader. The approach of using multiple time slots per node of a binary search tree is explored through three anti-collision protocols that aim to reduce the number of colliding responses from tags. This results in fewer reader queries and tag responses and, hence, energy savings at both the reader and tags (if they are active tags). An analytical framework is developed to predict the performance of our protocols, with the numerical evaluation of this framework validated through simulation. It is shown that all three protocols provide significant energy savings when compared to the existing query tree protocol while sharing the deterministic and memoryless properties of the latter