Traditional encryption and authentication methods are not effective in preserving a sink's location privacy from a global adversary that is monitoring the network traffic. In this paper, we first propose a novel anti-traffic analysis (ATA) method to preserve the sink's location privacy. In order to confuse a local or global adversary, each node generates dummy messages, the number of which is dependent on the number of the node's children. Hence, ATA is able to prevent the adversary from acquiring valuable information on the sink's location through the traffic analysis attack. However, a larger number of dummy messages lead to consumption of extra energy. Then, we design our improved ATA (IATA) in such a way that we select some sensors to act as fake sinks, to ensure that sensors around fake sinks generate dummy messages and discard received dummy messages. Since the problem of the optimal fake sinks' placement is nondeterministic polynomial time (NP)-hard, we employ local search heuristics based on network traffic and security entropy. Performance analysis of the ATA scheme can protect the sink's location privacy, and IATA scheme can reduce energy consumption.