In the manufacturing of high melting point glasses with volatile components, in particular of glasses from the group of boron glasses and borosilicate glasses, a furnace is provided that has a superstructure, fossil fuel burners, and a melting tank. In front of a conditioning zone and a throat leading to an extraction zone, a step-shaped raised area in the bottom is provided which is formed continuously over the complete width of the melting tank. In order to suppress segregation or, respectively, phase separation, to protect the furnace construction materials and to enable problem-free operation, a temperature of at least 1600.degree. C. is produced in the superstructure by means of oxygen-rich oxidation gas, a raised area is provided in the form of a refining bank with a step in front of it, the step being at least 150 mm high and from which at least one row of booster electrodes projects upwards, before the step, the melt flows over at least one row of bubblers located in the bottom, and behind the step, the glass flows in a highly heated state over the refining bank for a distance of 800 mm to 2000 mm, the upper side of said bank being at a maximum distance "T" of 300 mm from the glass bath surface.