Constant 2 Amps with good heatsinking for ~15minutes. It was really a waste of energy but just tried it.... on a U5U Luxeon. If it blew, it was no real loss.
1.6A+ for 20 minutes on 6xAA NiMH (R ranked Luxeon emitter, Vf=6.48 at finishing time). Mag2D body, Lambda heatsink, without reflector, laying on the desk.
Starting with 13.2W ending with 10.46W.
I have put up to 50 amps into a five watt and they take handle it quite well, but this was for very short periods of time (tens of microseconds). Very bright for a very short time. Anything over 56 amps and they would pretty consistently pop.
(pardon the noob, I've been reading for some time but not posting)