Trim excess fat from jointed rabbit and rinse with cold water. Pat dry with paper towels.
Pour brine solution ingredients into the brine bucket. Stir until sugar and salt have dissolved.
Place rabbit portions in the bucket. Cover and leave to brine in the refrigerator overnight.
Remove rabbit from brine. Rinse and pat dry.
In a small bowl, combine the dry rub ingredients. Use a fork to remove or crush any lumps that form.
Apply dry rub to the rabbit, covering generously all over and working into any folds of crevices along the meat surface.
Fire up the smoker to 225°F (107°C)
Once at target cooking temperature, place rabbit portions on smoker grates. Close the lid and cook until internal temperature is 160°F (71°C), about 1 hour.
Remove from smoker and rest for 10 minutes. Serve immediately and enjoy.