In one embodiment, a service function classifier device determines a classification of a packet using one or more packet classification rules. The device selects a service function path based on the classification of the packet. The device determines one or more traffic flow characteristics based on the classification of the packet. The device generates a service function chaining (SFC) header that identifies the selected service function path and the determined one or more traffic flow characteristics. The SFC header is configured to cause a device along the service function path to forward the encapsulated packet based on the identified service function path and the determined one or more traffic flow characteristics. The device sends the packet along the selected service function path as an encapsulated packet that includes the generated SFC header.