Originally Posted by Tiersten
It'd be more work but doing PWM will give you better control over brightness and waste less power than just putting in a variable resistor. One of the tiny 6-8 pin uCs like a PIC with a small FET would be more than capable of doing this.
True, but make sure it has a high enough clock speed. LED's with bad PWM can give you more of a headache than just reading an LCD screen.