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Overlay networks are central to the operation of large-scale decentralized applications, be it Internet-scale P2P systems deployed in the wild or cloud applications running in a controlled—albeit large-scale—environment. A number of custom solutions exist for individual applications, each employing a tailormade mechanism to build and maintain its specific structure. This paper addresses the role of randomness in developing and maintaining such structures. Taking Vicinity, a generic overlay management framework based on self-organization, we explore tradeoffs between deterministic and probabilistic decision-making for structuring overlays. We come to the conclusion that a pinch of randomness may even be needed in overlay construction, but also that much randomness or randomness alone is not good either.