Smoke is created by wood and its proximity to the lit. If 'smoke' is being created by the lit on the bottom, it's from the charcoal, not the wood, unless the wood is next to the lit.
The air is regulated, yes, but there needs to be air so that the lit will burn. With air present and the unlit above, the lit will light the unlit in short order, again, defeating the purpose of a slow, measured, easily controllable temp rise.
With a typical Minion start one simply places the lit on top, wood scattered about. Soon, the lit gets the wood going - plenty of smoke from the wood from the get-go.