Remove rabbit from the fridge about one hour before smoking to come down closer to room temperature. Rinse with cold water.Discard brine.
Pat meat dry with a paper towel.
Coat all surfaces of the rabbit with dry rub.
Set up smoker with wood chips or pellets. Preheat to 200°F / 95°C.
Place pieces directly onto the smoker rack.
Smoke rabbit for 5-6 hours until internal temperature reaches 160°F / 70°C. Measure temperature in the thickest part of the back thigh. Remove it from the smoker. Tent with aluminum foil. Let rest for at least 10 minutes. In the first 5 minutes, internal temperature should raise to 165°F / 73°C.