A glass-melting furnace (10) has an upstream end (6), a downstream end (8), and a roof (22). The upstream end is positioned upstream of the downstream end. A charger (32) is provided to supply glass-forming material (30) to the upstream end of the furnace. At least one burner (34) is provided to supply heat to the glass-forming material at the upstream end of the furnace. An exhaust (60) is in communication with the downstream end of the furnace, with the exhaust being positioned downstream of the at least one burner.