Separate dough into 4 rectangles (do not pull apart the "triangles" of dough). Place each sausage along the length of a dough rectangle, at the edge. Roll the dough around the sausage (the sausage ends will stick out). Pinch perforations and seams together.
Place dogs on barbecue preheated to medium heat. Grill 1 to 2 min,, turning once, to firm up the dough and get it grill-marked.
Transfer dogs to disposable aluminum foil tray placed on top rack of barbecue. Close lid. Cook, turning once, 12 to 15 min. until dough is golden brown and sausage is heated through. Serve with ketchup, mustard and relish, if desired.
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