1. In a large stockpot, dissolve salt and sugar in 1 gallon cool water. Place turkey, bone side up, in brine and weight it with a plate. Refrigerate 6 to 8 hours. Rinse turkey thoroughly under cool water and pat dry with paper towels.

2. Set up grill for indirect cooking. Place turkey on grill, away from hot coals; cover, keeping vent holes open over meat. Grill until cooked through, or an instant-read thermometer inserted in thickest part of turkey registers 165 degrees, about 1 1/2 hours (if using a charcoal grill, add a couple handfuls of charcoal every half hour to maintain heat). Let rest 10 minutes before slicing.