Actually you don't need a current limiting resistor for an LED. A while back I was experimenting with using the early Luxeon LEDS as a light source for high speed photography. I used a MOSFET to turn on the Luxeons with a low ESR caps as the voltage source for 10 uS. Worked fine for over ten thousand cycles. Only resistence was the ESR from the CAP (able to provide 5+AMPS) and the MOSFET resistance. The idea was to get the maximum output from the LED's and determine how long they would last.
The experiment failed because I couldn't get anywhere near the light output I can from an air gap spark.