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Brush alligator ribs with enough barbecue sauce to coat. Place ribs on a rack set in a baking pan. Cover with plastic wrap and then aluminum foil. Bake for 3 hours.
Remove alligator ribs from the oven. When cool enough to handle, remove the plastic wrap and cover loosely with the aluminum foil; allow the ribs to rest 20 to 30 minutes.
Meanwhile, prepare a smoker with your favorite type of wood chips. Transfer the ribs to the smoker and smoke for 30 to 45 minutes, depending on the size of the ribs; alligator ribs are very lean and dry out easily, so you may want to remove smaller ribs from the smoker first. After smoking, coat the ribs with more barbecue sauce.