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In the wireless sensor network (WSN) literature, the use of a mobile sink is commonly viewed as one of the most successful means of load balancing as well as an effective defense against the so-called hot-spot phenomenon. The aim of this paper is to investigate the real-world applicability of the known theoretical benefits associated with the use of mobile sink(s). In particular, we examine the pros and cons of deploying path-constrained mobile sink(s) in IEEE 802.15.4 / ZigBee-based WSNs.The main contributions of this paper are as follows: First, analytically and through simulation, we demonstrate that in idealistic (zero-overhead) networks the use of a mobile sink does result in a more even distribution of routing load and longer network lifetime, as earlier suggested in the WSN literature. Moreover, in small- to medium- size zero-overhead WSNs, the outer-peripheral and the diagonal-cross trajectory appear to be more effective than other types of mobile-sink trajectories. Unfortunately, real-world networks, including ZigBee WSNs, are not zero-overhead - these networks employ special mechanisms that generate additional (overhead) traffic in order to manage congestion and node mobility. The results of our OPNET-base simulation study demonstrate that in IEEE 802.15.4 / ZigBee WSNs, once all of the overhead traffic is accounted for, the theoretical advantage of deploying a mobile- vs. deploying a static- sink completely disappears. Hence, for anybody contemplating the use of a mobile sink in ZigBee sensor networks, the minimization of protocol overhead may have to be the first course of action. In the last part of the paper, we introduce two simple mechanisms for reduction of mobility-related overhead in ZigBee WSNs. The presented simulation results suggest that with these mechanisms in place the superiority of mobile- over static- sink deployment can be regained.