The invention is directed to a method of preventing isopipe sag when using the overflow drawdown fusion process for making flat glass sheets. The method applies a vertical restraint on at least one end of an isopipe resting on a support to thereby reduce sage and/or the rate of sag during use of the isopipe. Using the vertical restraint block in accordance with the invention, the sag and/or rate of sag has been found to be reduced by at least 40 percent relative to an isopipe that does not use the vertical restraints of the invention or a compressive force along the sides of the isopipe.