Many structured overlay networks rely on a ring invariant as a core network connectivity element. The responsibility ranges of the participating peers and navigability principles (greedy routing) heavily depend on the ring structure. For correctness guarantees, each node needs to eagerly maintain its immediate neighboring links - the ring invariant. However, the ring maintenance is an expensive task and it may not even be possible to maintain the ring invariant continuously under high churn, particularly as the network size grows. Furthermore, routing anomalies in the network, peers behind firewalls and Network Address Translators (NATs) create non-transitivity effects, which inevitably lead to the violation of the ring invariant. We argue that reliance on the ring structure is a serious impediment for real life deployment and scalability of structured overlays. In this paper we propose an overlay called Fuzzynet, which does not rely on the ring invariant, yet has all the functionalities of structured overlays. Fuzzynet takes the idea of lazy overlay maintenance further by dropping any explicit connectivity and data maintenance requirement, relying merely on the actions performed when new Fuzzynet peers join the network. We show that with sufficient amount of neighbors (O(log N), comparable to traditional structured overlays), even under high churn, data can be retrieved in Fuzzynet w.h.p. We validate our novel design principles by simulations as well as PlanetLab experiments and compare them with ring based overlays.