The L2 head is a "dumb" head and just contains the LED. The regulation is in the body. The KL1 does not fit on the L2 body. There's a fairly wide plastic cylinder in the center of the KL1 that prevents fitting. The L2 head physically (and electrically) fits on the E1x/E2x/L4 bodies, but since there's not even a resistor in the L2 head, AFAIK, you might be risking damage to the LED (the L2 does not light up with the one CR123 of the E1. The output on the E2 with two CR123 is fairly low, like the low mode of the L2. Damage risk might actually be low, but I would not recommend it for standard usage).