Abstract: A glass sheet tempering method and resultant glass sheet are disclosed as being provided by modulated quenching that initially cools the oppositely facing surfaces of a conveyed glass sheet at a first cooling station (14) with a first rate of heat transfer for a finite time to cool the surfaces from tempering temperature to below the strain point without cooling the center of the glass sheet below the strain point. Thereafter the oppositely facing surfaces of the conveyed glass sheet are cooled within a second cooling station (15) at a second rate of heat transfer less than the first rate to initially cool the center of the glass sheet below the strain point without corresponding surface cooling, and thereafter further cools the center and the sruface. The second rate of heat transfer is of a magnitude so that the surface temperature initially increases without going back substantially above the strain point prior to subsequently again cooling.