An external-electrode discharge lamp has a light-permeable, electrically insulative outer casing having a closed hollow space defined therein. A discharge medium is sealed in the outer casing. An external electrode is disposed on an outer surface of the outer casing for causing a dielectric barrier discharge in the discharge medium. The external electrode comprises a plate of an electrically conductive material and is brazed to the outer surface of the outer casing by a brazing material disposed fully circumferentially on the outer surface of the outer casing.