How many distinct values you want?
The Arduino ADC reads 1024 different values and you may consider the last one to three noise (depends) leaving effectively 128-256 distinct values.
If your sketch uses two potmeters, one for bigsteps and the other for fine tuning you could have more steps.
unsigned int val = (analogRead(POT1) /4) * 256 + analogRead(POT2)/4; // DO NOT OPTIMIZE the /4 and the *256 !!!
you could also use an averaging read for both POT's, which is left as an exercise 