The invention enables an LSP or embedded LSPs to be mapped directly to an SPVC and carried over the ATM network. A unidirectional SPVC is established by associating it to a particular ingress LSP at the SPVC source endpoint on a multi-service switch, and to an egress LSP on the SPVC destination endpoint on another multi-service switch. The information necessary to establish the SPVC is appended in the SPVC setup message and includes LSP specific information such as the far end router ID and LSP label information, be it transport label or the full label stack. The information in the modified setup message is then used by the destination endpoint to find and connect the SPVC to the correct LSP. Incoming traffic from the LSP is switched to the SPVC at the source endpoint. The SPVC carries this traffic through the ATM network, and then the traffic is switched to the egress LSP when it emerges from the ATM network at the destination endpoint.