In the thread "Using a variable resistor to dim an LED", Phil Frost provides almost the answer I need, and even provides a great diagram, but he's working from a 5V supply.

My question concerns what the resistor values would be for a similar circuit running a red LED from a 3V power supply.  I'm pretty sure the fixed resistance would be less, and I know how to calculate the 'drop' resistance for a fixed-brightness LED, but I'm not an EE, and I'm not sure I understand the relationship between the fixed and variable resistance values in the circuit.

My project is a simple dimmer for a "unit-power finder" to be mounted on a astronomical telescope.  The LED does not need to reach its full brightness as it's being used to back-illuminate a film reticle which is being projected against the night sky.  Fine control at the dim end of the range would be a plus.

I'd use an arduino based dimmer/pulser circuit, except all the good toys are still packed from a recent move, and I need something quicker and dirtier for the time being now that we're approaching prime observing weather.

Thanks in advance