Pulldown Resistor for 10K pot

I'm trying to make a pulldown resistor for my 10K pot on the arduino due, but I don't know what resistance resistor to put in. I'm using the 3.3V line for power on the pot, so the typical value of 10K pulls the input down a bit too much and instead of a linear input, the middle reads 96 (out of 1024). Can anyone offer any help?