An offset barbeque smoker grille has an openable cover shaped as the elongated back portion of a quadruped and the products of combustion are applied to meat on said grille with the cover closed and at least one restrictor is included in said fourth flow path to hold smoke in contact with said meat wherein a meat treatment apparatus is used as a smoker. The cooking and smoking uses counter flow from the firebox near the head of the quadruped under the cooking and smoking chambers toward the rump of the quadruped and back over the top of the cooking chambers to provide even cooking.
