[sam_who]

You could power a 10-turn pot with 12 volts. That will give you 1.2 volts per turn.

CAUTION! If you choose this method, you must ensure not to go past ~4 turns or you risk burning the input (for starters). Also, you have to use the lower end of the pot (0-4.8 volts) rather than the upper (7.2-12 volts).

Finally, take the advice offered earlier and get a higher value pot.