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ZigBee is a communication standard which is considered to be suitable for wireless sensor networks. In ZigBee, a device (with a permanent 64-bit MAC address) is said to join a network if it can successfully obtain a 16-bit network address from a parent device. Parent devices calculate addresses for their child devices by a distributed address assignment scheme. This assignment is easy to implement, but it restricts the number of children of a device and the depth of the network. We observe that the ZigBee address assignment policy is too conservative, thus usually making the utilization of the address pool poor. Those devices that cannot receive network addresses will be isolated from the network and become orphan nodes. In this paper, we show that the orphan problem can be divided into two subproblems: the bounded-degree-and-depth tree formation (BDDTF) problem and the end-device maximum matching (EDMM) problem. We then propose algorithms to relieve the orphan problem. Our simulation results show that the proposed schemes can effectively reduce the number of orphan devices compared to the ZigBee strategy.