When I loosen the cable, it doesn't allow the derailleur to move out enough to use the highest gears without the chain rubbing.
Where's it rubbing ?
Possibly it's the way you're using the shifter and not the derailleur.
I presume you've got rapidfire shifters.
When shifting up chainrings are you using the shifter by just clicking it to it's next index position ?
If so that might be the problem.
When pushing on the shifter with your thumb to change up to the next chainring, the shifter will click into it's next position but it also allows you push a bit further pulling more cable to help get the chain get onto the next chainring, when the chain has been grabbed by enough teeth to allow it to wrap around the chainring you release your thumb, the cable then releases back where the shifter clicked to and the derailleur moves back to it's indexed position.