A method for driving a gas discharge lamp (1) is described, wherein electric first DC power is provided at a relatively high voltage and a relatively low current. Said first power is converted down to second DC power at a relatively low voltage and a relatively high current. Said second power is fed to a gas discharge lamp, preferably via a commutator. The conversion of said first power to said second power is performed in at least two steps, a first one of such steps including the step of converting down said first power to an intermediate DC power at an intermediate DC voltage lower (VM) than said first DC voltage but higher than said second DC voltage. A downconverter device (30) for use in a driving apparatus (10) for a gas discharge lamp (1) is described. The downconverter device comprises at least two downconverter units (31, 32) connected in series, for converting down said intermediate DC power to said second power.