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Distributed hash table (DHT) systems are an important class of peer-to-peer routing infrastructures. They enable scalable wide-area storage and retrieval of information, and will support the rapid development of a wide variety of Internet-scale applications ranging from naming systems and file systems to application-layer multicast. DHT systems essentially build an overlay network, but a path on the overlay between any two nodes can be significantly different from the unicast path between those two nodes on the underlying network. As such, the lookup latency in these systems can be quite high and can adversely impact the performance of applications built on top of such systems. In this paper, we discuss a random sampling technique that incrementally improves lookup latency in DHT systems. Our sampling can be implemented using information gleaned from lookups traversing the overlay network. For this reason, we call our approach lookup-parasitic random sampling (LPRS). LPRS converges quickly, and requires relatively few modifications to existing DHT systems. For idealized versions of DHT systems like Chord, Tapestry, and Pastry, we analytically prove that LPRS can result in lookup latencies proportional to the average unicast latency of the network, provided the underlying physical topology has a power-law latency expansion. We then validate this analysis by implementing LPRS in the Chord simulator. Our simulations reveal that LPRS-Chord exhibits a qualitatively better latency scaling behavior relative to unmodified Chord. The overhead of LPRS is one sample per lookup hop in the worst case. Finally, we provide evidence which suggests that the Internet router-level topology resembles power-law latency expansion. This finding implies that LPRS has significant practical applicability as a general latency reduction technique for many DHT systems. This finding is also of independent interest since it might inform the design of latency-sensitive topology models for the Internet.