Hi Enki:
I think something like this is the answer.  The specs say 2.8 to 12 volt 
operation (notice not 1.5 V) and 1 Watt power, so it's not really a joule theif.

Hi Martin:
No Scope needed.  Just look at the bench supply meters as the voltage is 
changed.  Data at: http://www.prc68.com/I/LED.shtml#E10LED
shows constant 1 watt power load.  $8 Superbrightleds.com  T10-WHP

Hi Olin:
Thanks for the new link, I've updated my page.

Hi David VanHorn:
Yes.  I think of Switching Mode Power Supplies as transformers for DC.

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