Methods of fabricating flat glass with low levels of warp

A method of fabricating glass sheets (13) is provided in which the sheets are cut from a glass ribbon (15) composed of a glass having a glass transition temperature range (GTTR). The ribbon (15) is formed by a drawing process in which edge rollers (27a,27b) contact the glass ribbon (15) at a location along the length of the ribbon where the temperature along the center line (17) of the ribbon (15) is above the GTTR. The edge rollers (27a, 27b) locally cool the ribbon (15), and the cooling produces a sine wave type buckling (S warp) along the edges of the glass sheets (13). The S warp is reduced or eliminated by heating the bead portions (21a, 21b) of the ribbon (15) and/or portions of the ribbon (the S warp portions 25a and 25b) which are located next to the bead portions (21a, 21b) and/or by cooling the center portion of the ribbon (15) at least one location along the length of the ribbon (15) where the temperature at the ribbon's center line (17) is within the GTTR.