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Gossip, or epidemic, protocols have emerged as a highly scalable and resilient approach to implement several application level services such as reliable multicast, data aggregation, publish-subscribe, among others. All these protocols organize nodes in an unstructured random overlay network. In many cases, it is interesting to bias the random overlay in order to optimize some efficiency criteria, for instance, to reduce the stretch of the overlay routing. In this paper, we propose X-BOT, a new protocol that allows to bias the topology of an unstructured gossip overlay network. X-BOT is completely decentralized and, unlike previous approaches, preserves several key properties of the original (nonbiased) overlay (most notably, the node degree and consequently, the overlay connectivity). Experimental results show that X-BOT can generate more efficient overlays than previous approaches independently of the underlying physical network topology.