Rich - if you are going to add smoke, do it at the beginning - that's when the meat will absorb the most smoke flavor. Don't overdo it though - tender meats like that can over absorb the smoke and that doesn't taste so good. Also, when you do smoking on the gasser, crack the lid a bit, otherwise the smoke will taste bitter. You want the smoke to pass by/ thru the meat, not settle on it.
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