Techniques for controlling packet flows are described. In an example, a packet is sent on a virtual network. The packet's header includes scoping data that indicates a network boundary within which the packet is permitted and/or prohibited to flow. A network virtualization device of a substrate network receives the packet. The network virtualization device determines the scoping data from the header and, based on network configuration information, determines the forward flow of the packet. If the forward flow falls within a permitted network boundary indicated by the scoping data, the network virtualization device sends the packet forward. Otherwise, the packet is dropped.