An improved method for the heat treatment of quartz-glass tubes at temperatures above 1200.degree. C. is disclosed wherein a pressure is maintained within the glass tube which is 3 to 110 mm Hg higher than the pressure on the external surface of the quartz tube over the heated area of the tube for at least the length of time that a temperature of 1200.degree. C. is exceeded. The process is particularly useful for the treatment of quartz-glass tubes within which silicon wafers are disposed for the purpose of diffusing doping agent into silicon wafers or of depositing doped epitaxial layers on silicon wafers.