A method is provided in one example embodiment and includes receiving at a network element a packet including a Network Services Header (“NSH”), in which the NSH includes an Infrastructure (“I”) flag and a service path header comprising a Service Index (“SI”), and a Service Path ID (“SPI”) and determining whether the I flag is set to a first value. The method further includes, if the I flag is set to the first value, setting the I flag to a second value and forwarding the packet to the service function that corresponds to the SI for processing. The method still further includes, if the I flag is not set to the first value, decrementing the SI and making a forwarding decision based on a new value of the SI and the SPI.