yeah that sounds like a resistance problem. do you know the voltage and the amperage of the 10mm?? id get a ohm meter and check the resistance of the lights.
If all of this is sounding like jibberish then go to google and look up led info and wiring techniques
does your existing system already have resistors built into it ?
if you tied in the new ones with resistors maybe, just maybe you got twice the resistance that they need.
check the resistance in your existing system to make sure, if it is already there, take out the newly added resistance and get your brightness you want.
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Okay, I have done some searching on Google, dogpile, etc. I have got a basic idea of what to do, but it seems like the articles are either really basic or in depth. I was hoping to add an LED light (or two) to each cup holder. I was originally thinking I would simply wire them to the cigarette lighter. This was because it is very close, will only be on with the ignition, and would be adequate power. Now I am thinking it is too much power. Anyone have suggestions, knowledge, advice to offer?
make sure the leds you are installing are wired correctly together... because if the leds are wired in series the light will be dimmer as opposed to having them wired in parallel which should make it brighter