Dynamically by-passing a service function instance on a service chain after the service function instance has processed the first few packets of a traffic flow may improve the overall processing efficiency of the service chain. When using a control plane mechanism, a service function instance communicates a by-pass indication to a control plane entity to prompt the control plane entity to re-route remaining portions of the traffic flow around the service function instance. When using a data plane mechanism, a service function instance includes a by-pass indication in a service chain header (SCH) of a packet in a traffic flow, and forwards the packet to a data plane entity. The by-pass indication will prompt the data plane entity to re-route remaining portions of the traffic flow around the service function instance.