Im with FIU on this one. I burn wood only in my stick burner. If there is too much smoke, I say its one of 2 things. Wood not being seasoned (dry) long enough or too much flavor wood, like Hickory being used and giving the meat an overly smoked taste.
Oak in itself is a very neutral wood, imparting a very subtle flavor, which is why is make a great wood to use. Adding small chunks of flavor woods in the process is where the meat really gets its smoky flavor from.
When using wood, it has a tendency to billow white. Especially when being added to an existing fire and the wood goes thru a process of heating up and burning off any residual moisture and other natural chemicals in the wood. For that reason, many choose to either preburn thier wood, which is nothing more really than making a fire with the wood you intend on using, letting it get fairly charred then extinguishing it and using it them. Others will take any wood they are going to use and if they can, set it on top of or inside the firebox away from the fire and let it heat up. This drives excess moisture out, and brings the temp of the wood way up, close to the point of igniting without actually doing so. When it comes time to add wood, one of these pieces are thrown in the piece will ignite within a few seconds.
You can make a fire burner if you just want to use hot coals. Basically its a 55 gal drum, cut in half. A few pieces of rebar are run thru to make a grate making squares approx 6 by 6 inches. This is up off the bottom say a foot. Build a fire as normal, and when the hot coals burn down and fall thru, you just scoop them up and add them to the firebox.
Some will swear by it and it really boils down to whether it works for you. I have done and that is how I started out, but I have since found that building and maintaining a small, manageable fire gives me superior results. I make my fires with the method I described above. Pre-burning all my wood, and keeping it either on top of my firebox or inside the firebox out of the reach of the flame. Wood is within a few degrees of igniting and when I add a piece, it lights up almost instantly, with zero white or overpowering smoke. For flavor wood, I add a fist size chunk a few inches from the fire, close enough so it just smolders but far enough away to it won't catch fire.
That's my story and I'm sticking to it