Set up an outdoor grill for indirect grilling, placing a large foil drip pan in the center.

If using a smoker, light and set it up according to manufacturer's instructions and heat to 275 degrees Fahrenheit.

In a smoker, cook the bird for 3 1/2 to 4 1/2 hours.

Drain the brined turkey.

Blot the turkey dry inside and out and truss if desired.

Place the turkey in the center of the grill grate, over the drip pan and between mounds of natural lump charcoal.

Toss 1/2 cup of soaked wood chops on each mound of coals.

Place lid on grill.

Adjust vents to keep the temperature between 325 and 350 degrees Fahrenheit.

Grill the turkey until darkly browned and cooked through, approximately 2 1/2 to 3 hours.

Baste the turkey with melted butter after the first hour and every hour thereafter.

If the skin starts to brown too much, loosely tent the bird with foil.

Use an instant-read thermometer to test for doneness; the turkey is ready when the internal temperature of the thigh is 180 degrees Fahrenheit.

Replenish charcoal every hour, adding 8 to 10 lumps of charcoal to each mound of coals and leaving the grill uncovered for a few minutes to allow the charcoal to light.

After 1 hour, add 1 1/2 cups of soaked wood chips.

Transfer the turkey to a platter, loosely tent with foil, and let rest for 10 minutes before carving.

Reserve any drippings in the drip pan for gravy.