I received a a lot of comments on my Supercharged Joule Thief circuit, which gives an efficiency of up to twice that of a conventional JT (more about this in my blog where I switch between JTs and measure the light output). The SJT requires a few additional components, nothing out of the ordinary. Essentially, it rectifies some of the output to the LED, and uses this to supply the DC bias to the transistors base, through the feedback winding. I’ll post a schematic of it here.
I have built many of these SJT circuits and verified that it really does work better than a conventional JT (see the link above). The two additional parts are the 1N4148 diode and a capacitor with a value in the 470 to 1000 pF range. The cost is about $0.10 US. The resistor value of 1.5k is the optimum point between efficiency and light output.