A honeynet is a portion of routed but otherwise unused address space that is instrumented for network traffic monitoring. It is an invaluable tool for understanding unwanted Internet traffic and malicious attacks. We analyze the problem of defending honeynets from systematic mapping (a serious threat to their viability) as a simple twoperson game. Our theoretical ideas provide the first formalism of the honeynet monitoring problem, illustrate the viability of network address shuffling, and inform the design of next generation honeynet defense systems.