A converter for powering a discharge lamp of a motor vehicle headlight, the converter comprising a primary circuit and a secondary circuit which includes two branches connected in parallel, each of which is coupled by mutual induction with the primary circuit, and two diodes connected in such a manner as to prevent either of the branches discharging into the other, the transformation ratio by mutual induction with the primary circuit of one of the two branches being greater than the transformation ratio of the other, the branch having the greater transformation ratio including a switch controlled by control electronics in such a manner as to be on whenever the voltage of the lamp is greater than a given threshold voltage, and to be off whenever said voltage becomes less than said threshold.