A method for forming a cold spot region on a discharge tube of a discharge lamp is disclosed. In the method, a discharge tube is formed, and a tubular extension is formed on at least one end of the discharge tube. The tubular extension has a smaller diameter than the diameter of the discharge tube end. The tubular extension is formed so that a free end of the tubular extension extends away from the end of the discharge tube. A reduced thickness portion is formed on the tubular extension. The reduced thickness portion is formed as a membrane.A discharge lamp is also disclosed, which comprises a discharge tube with a tubular extension located at an end of the discharge tube. The tubular extension has a smaller diameter than the diameter of the discharge tube end, and the tubular extension comprises a reduced thickness portion. The reduced thickness portion is a membrane, preferably formed of the material of the tubular extension.