Laminated glazing includes a first glass sheet constituting an external face of the glazing, connected to a second glass sheet by a first interlayer adhesive layer, the edge of the first glass sheet being set back with respect to that of the second, a peripheral part of the free surface of the first glass sheet, its edge face, that of the first interlayer adhesive layer and a part of the surface of the second glass sheet extending beyond the first describing a continuous stepped contour which is covered, with interposition of adhesive, with a stepped element made of polymer material which can contain reinforcing fillers, which exhibits a permeability to water vapor at most equal to 5 g/m2/day.