The F1 engine [1] (Saturn V, first stage) used another interesting way to improve efficiency with a gas generator cycle: using the turbopump exhaust gas as a cooling film in the engine nozzle. The fuel-rich exhaust was relatively cool compared to the flame generated by the rocket engine itself, and thus protected the nozzle from the most intense heat.
This is why, close up, the flame looks almost black close to the nozzle [2].
This is called film cooling, and SpaceX actually does use it on their second stage engine, the Merlin vacuum variant (MVac). You can see the beautiful exhaust plenum wrapping around the nozzle [1].
This isn't used for the regeneratively-cooled portion of the nozzle, but for the large radiatively-cooled nozzle extension, visible here [2].
This isn't used for the regeneratively-cooled portion of the nozzle, but for the large radiatively-cooled nozzle extension, visible here [2].
[1] http://imgur.com/HvtBYIi
[2] https://i.stack.imgur.com/9qIFO.jpg