In recent years peer-to-peer (P2P) technology has been adopted by Internet-based malware as a fault tolerant and scalable communication medium for self-organization and survival. It has been shown that malicious P2P networks would be nearly impossible to uncover if they operated in a stealth mode, that is, using only a small constant number of fixed overlay connections per node for communication. While overlay networks of a small constant maximal degree are generally considered to be unscalable, we argue in this paper that it is possible to design them to be scalable, efficient and robust. This is an important finding from a security point of view: we show that stealth mode P2P malware that is very difficult to discover with state-of-the-art methods is a plausible threat. In this paper we discuss algorithms and theoretical results that support the scalability of stealth mode overlays, and we present realistic simulations using an event based implementation of a proof-of-concept system. Besides P2P botnets, our results are also applicable in scenarios where relying on a large number of overlay connections per node is not feasible because of cost or the limited number of communication channels available.