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Applications such as VoIP need to provide anonymity to clients while maintaining low latency to satisfy quality of service (QoS) requirements. Existing solutions for providing anonymity such as mix networks are not well suited to applications like VoIP, SSH, and gaming which require low communication latency. This paper investigates the problem of on-demand construction of QoS sensitive routes on anonymizing networks using the VoIP application. We first describe triangulation based timing analysis attacks on shortest path route set up protocols. We show that even when a small fraction (~1%) of the network is malicious, the adversary can infer the source (caller) with reasonably high probability. Second, we describe random walk based route set up protocols that significantly improve anonymity while satisfying latency- based QoS guarantees. We describe a prototype implementation of our proposal and show that our protocols can significantly reduce the probability of inferring the caller. We present a detailed experimental evaluation to demonstrate our attacks and quantify the performance and scalability of our guards.