Disclosed herein is a system for supporting self-closing tongs specially adapted for gripping thin glass sheets (4.5 millimeters and less) during thermal processing, such as that involved during press bending wherein the glass sheets are brought to a sudden start and a sudden stop that promotes swinging of the tongs and its supported glass. The present invention limits the tong swinging so that the glass sheets can be aligned with small tong receiving notches in press bending molds, thereby improving the conformity of press bent glass sheets to their desired shapes.