I took a Ultrafire BJ08A which can use either a single AA or a single 14650. It has a XRE in it.
The light is a cylinder so it’s the size of a lipstick tube roughly. I replaced the reflector with a 19 mm (as I recall) aspheric lens.
That’s a cheap and easy way to get a small focused light. If you can make the light direct drive I’m sure it would throw even further (using 14650)
No light that size is going to be a tremendous thrower but it’s not bad for the size.
I bought the light at T-mart so the shipping was fast. I use it when hiking with a headlamp when I want a little more throw but when weight is an issue and I don’t want to carry a bigger light.
Otherwise I just use a 18650 with an aspheric I took out of a zoomie light.
I don’t like the rings in zoom lights so this was my solution.
Here was my write-up for the first light mentioned:
This was my write-up for the second light mentioned: