The invention describes a method of shutting down a high pressure discharge lamp (1) in which a pair of electrodes (2) is disposed in an arc tube (3), which method comprises reducing, upon receipt of a shut-down request (SR), the lamp power (P) towards a reduced power level (PR) required to sustain a long-term arc discharge between the electrodes (2), and driving the lamp (1) towards the reduced power level (PR) for a reduced power duration before completely shutting down the lamp power (P), whereby, prior to reducing the lamp power (P) towards the reduced power level (PR), the lamp power (P) is reduced to an undershoot power level (Pu), which undershoot power level (Pu) is lower than the reduced power level (PR) required to sustain a long-term arc discharge between the electrodes (2), and the lamp is driven at this undershoot power level (Pu) for an undershoot power duration (tu) before increasing the lamp power (P) again to approach the reduced power level (PR). Moreover the invention describes an appropriate driving unit (4) for driving a high pressure discharge lamp (1) and an image rendering system (40), particularly a projector system, comprising such a driving unit (4).