Higher accuracy joystick

I'm examining a 2-axis analog joystick I found. Basically it has two outputs that vary between 2V and 3V (centred about 2.5V) as the joystick position changes - there's an internal variable potential divider on each channel.
I can see the change between 2-3V easily enough using Arduino analog pins in a basic setup, but I can't think of an easy way to shrink the range the Arduino reads from natively 0-5V (internal ref) to 2-3V to improve the accuracy of the reading. I imagine some kind of potential divider is in order but my brain's not cooperating. Can anyone help?

You need an op-amp circuit to expand the +/- 0.5V out to +/- 2.5V.
Example article:

Normally an AC signal would be offset and then the signal amplified, a summing amplifier would be good for that
http://masteringelectronicsdesign.com/the-transfer-function-of-the-summing-amplifier-with-n-input-signals/

In this case, you already have the offset, and you want to maintain that, I have to think some about that. The joystick is pretty much a DC output level (very slowly changing relatively speaking) so I don't think running it thru a cap to remove the DC and then summing the changing part with a small DC offset that could then be multiplied in total would work, I would think the cap would just tend to filter the slowly changing +/- 0.5V as well.

Thanks CrossRoads. I'll run your circuit through some Horowitz and Hill and determine some values - it'll be a great exercise.