First, understand that whether or not you'll have fuel surcharges on your award tickets depends on both the miles you're using and the airline you're using them to fly. (freakinflyers.com)
You see, some mileage programs include these fuel surcharge fees on award tickets and some do not. (freakinflyers.com)
Note you also are not eligible for free upgrades on award tickets. (singleflyer.com)