A method of evacuating flat glass panels through a small pumpout tube is described. In order to avoid breakage, the end of this pumpout tube, which is located outside a bakeout oven, has to be mounted in an O-ring fitting, which exerts little force on the tube during evacuation and bakeout. This is achieved first by allowing axial movement of the tube within the O-ring fitting, and second by attaching the vacuum fitting to a bracket, which in turn is fixed to a metal vacuum cup on the glass panel inside the oven. This method has several advantages over conventional evacuation techniques, including enabling the pumpout tube to be situated in a protected location in the edge of the glass panel, and permitting the panel to be baked at high temperatures.