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We consider inferring the underlay topology among a group of hosts by traceroute-like end-to-end measurement tools. Since pair-wise traceroutes among hosts take a long time and generate much network traffic, Max-Delta has been proposed to infer a highly accurate topology with a low number of traceroutes. However, there is still high measurement redundancy in Max-Delta. That is, a router may be repeatedly visited in different traceroutes. In this paper, we integrate a previously proposed Doubletree algorithm into Max-Delta to reduce such redundancy. We study two key issues in the integration, i.e., the selection of h (a parameter of Doubletree) and the distribution of the global stop set of Doubletree. We have conducted extensive simulations on Internet-like topologies to evaluate the proposed scheme. The results show that Doubletree can significantly reduce the measurement redundancy and the bandwidth consumption in Max-Delta while introducing a small penalty in the measurement accuracy.