Hello.
LEDs don't require a specific voltage but a specific current, that with the JC-LED controller it is around 20mA. at full brightness.
This virtually works with all the leds.
Some bigger leds are built with smaller leds in series. this could not work, but we are talking about leds that are quite big, 20 or 30mm diamter.
if you have a link to a led that you are interested in, I can have a look.
Regards
Cristiano