Originally Posted by legendaryhog
This is good advise. You don't want green wood. Also, having a cleaner and/or hotter fire will give you the thin blue smoke that you are looking for. This doesn't mean that your cooker area where your food is needs to be hotter, that is another challenge itself, but that your fire chamber be burning efficiently. Look at your smoke coming out of your chimney next time. If it is thick and white, and not thin and blue you are going to get a heavy smoke flavor and possibly some "off" flavors.
You can limit smoke penetration by wrapping in foil or butcher paper partway through your cook. However, my guess is that your smoke isn't thin and blue and is a bit harsh.
It was thin and blue probably 50% of the time, thin (but slightly thicker) but white the rest of the time -- didn't get the big, billowing white smoke that I was worried about. So it wasn't terrible, but I think you're right, I could get it a little bit cleaner.
I'm guessing a bit of time for the wood to season will help.
Really appreciate the input everyone.