The invention relates to a device and a method for gravity-bending a glass sheet or stack of glass sheets having a plurality of sides, referred to as the glass, comprising a frame for bearing the glass in the peripheral zone thereof by means of a contact track, said contact track having concave curvatures at each of the sides of said frame, and a counter-frame that can make contact with the glassin the central zone of at least one side of the peripheral zone of the upper main face of the glass. The invention is particularly useful for bending thin glass and for reducing the ripples that tendto form towards the middle of the sides.