A method for operating a projection system (1) is described, wherein a brightness level (B1, B2, B3, B4, B5, B6) in an image (IM) is represented by the total length of a number of light switch-on phases within a particular image cycle (VT). A high pressure discharge lamp (2) of the projection system (1) is operated via a lamp driver with an essentially square-wave alternating current (IL) SO that an overshoot sequence (0), which occurs in the alternating current (IL) after a current zero crossing during operation of the high pressure discharge lamp (2), has a frequency so high that for each possible brightness level at least one full period (P) of the overshoot sequence (0) lies essentially within a light switch-on or switch-off phase (ts) following the zero crossing. A projection system (1) and a lamp driver (10) for a high pressure discharge lamp (2) in such a projection system (1) are also described.