A rod-core transformer for use as a starting transformer in the cap of a high-pressure discharge lamp for a motor vehicle headlight. The rod-core transformer has at least two cores (2, 3) which are in the form of rods and are arranged alongside one another, and on each of which a multilayer secondary winding (4, 5) is wound, with the respective layers (4a, 4b, 4c, 4d) and (5a, 5b, 5c, 5d) being connected in parallel and being arranged one above the other without any offset. Furthermore the secondary windings (4, 5) are electrically conductively connected to one another, with their total resistance being at most 2&OHgr;. The transformer is particularly highly suitable for use as a starting transformer for high-pressure discharge lamps with a low operating voltage, for example halogen metal-vapor high-pressure discharge lamps which do not contain mercury.