A strengthened glass or glass ceramic sheet has a roughness of greater than 0.05 nm Ra and less than 0.08 nm Ra over an area of 10 μm×10 μm and has the property that, excluding areas within three sheet thicknesses of the outer edge surface of the sheet, the slope of a measured value of a thermally affected property of glass over distance along the first major surface of the sheet is higher bordering one or more lower-cooling-rate-effect-exhibiting areas on the first surface of the sheet than elsewhere on the first surface of the sheet, and at least one of said one or more areas has a shortest linear dimension, in a direction parallel to the first major surface, of less than 100000 μm.