How about 2, 2 ohm resistors in parallel?
Or the most simple, just coughing up 99cents and buying a 1 ohm 2W resistor
@jkwilborn Thanks for the ideea, but @Grumpy_Mike said that resistors cannot be used in this case, and if anyone think otherwise it's an idiot. 
That doesn't solve the problem of a lower LED current with declining battery voltage.
They are meant to be used in a flashlight.
The wires connect to the LED.
The battery(+) is pushed against the circle underneath.
The edge of the board touches the metal case of the torch, and so negative of the battery.
Leo..
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Got it...
Looks like you are limited if you wish to have proper voltage when the supply voltage drops..
Good luck
Thank you @Wawa ! The LED works with this thing connected to it.
I used to be into this stuff 25 years ago and am getting back into it again, so forgive me if I am wrong. Your LED should light up without a resistor at all, but will have inconsistent brightness and may burn out. A resistor solves the burn out problem, but not the inconsistent brightness problem. A constant current LED driver solves both problems, but then you need to supply more voltage than your battery can supply.
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Especially with Lithium Ion batteries, since they usually have incredible peak current capability. The cheap pen flashlights that use AA and AAA or coin cell batteries and have no resistor, depend on the large internal battery resistance to avoid burnout.
Thank you @asyork !
Post#19 has a link to an AMC7135 CC driver with minimal dropout at low batt voltage.
Leo..
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