The Tall Box Burner has four stacking layers—a base for storage of short or long incense sticks, an ash catch, an incense holder with special opening that allows stick remnants to drop into ash catch, and a cover with a slot for release of smoke. When stacked, the long slots on the sides allow air flow. The cover has a faceted surface on the interior that guides the smoke to the slot. The cover conceals the burning stick and the ash below. If preferred, the cover can be left off during burning. The holder works for a variety of stick diameters, and positions of the stick. When burning with the cover on, the incense sticks should be placed as horizontal as possible.