The high-pressure discharge lamp comprises a discharge vessel provided with a first and a second lamp electrode, an outer envelope which surrounds the discharge vessel with space and which is provided with a lamp cap. A tube-like UV enhancer having a longitudinal axis is provided in the space having a ceramic wall and provided with an internal enhancer electrode connected to the first lamp electrode and by way of a capacitive coupling connected to the second lamp electrode, and which enhancer electrode has an end inside the enhancer. The capacitive coupling is formed by a metal curl positioned around the UV enhancer in a plane perpendicular to the longitudinal axis of the UV enhancer and close to the end of the enhancer electrode. The lamp shows on ignition with a relative small ignition voltage only a very small ignition delay.