The security of a network configuration is based, not just on the security of its individual components and their direct interconnections, but it is also based on the potential for systems to interoperate indirectly across network routes. Such interoperation has been shown to provide the potential for cascading paths that violate security, in a circuitous manner, across a network. In this paper we show how constraint programming provides a natural approach to expressing the necessary constraints to ensure multilevel security across a network configuration. In particular, soft constraints are used to detect and eliminate the cascading network paths that violate security. Taking this approach results in practical advancements over existing solutions to this problem. In particular, constraint satisfaction highlights the set of all cascading paths, upon which we can compute in polynomial time an optimal reconfiguration of the network and ensure security.