Clocked flyback converter circuit for operating one or more lamps, comprising a controllable switch, a transformer having a primary winding coupled to the controllable switch and a secondary winding to which the lamps can be coupled, a control unit for actuating the switch, and means for directly or indirectly detecting the current through the switch in the switched-on state and for supplying a signal representing this current to the control unit, characterized in that the control unit is configured to actuate and switch off the switch in limit operation and in discontinuous operation when the signal representing the current has reached a variable switch-off threshold, to modify the switch-off threshold in limit operation in order to modify the power transmitted by the flyback converter circuit, to reduce the switch-off threshold for the current signal only to a minimum value (I min), and to change from limit operation into discontinuous operation in order to achieve a further reduction of the power transmitted by the flyback converter circuit when the switch-off threshold is fixed at the minimum value (I min), wherein a dimming signal can be supplied to the control unit, and the control unit is designed, in limit operation, to modify the switch-off threshold (Is) according to the dimming signal, and, in discontinuous operation, to modify the time of switching the switch back on according to the dimming signal when the switch-off threshold (I S) is fixed at the minimum value (I min), and wherein the transformer has a primary-side auxiliary winding to which the control unit is coupled in order to detect a voltage curve across the auxiliary winding, and in discontinuous operation, the control unit switches the switch back on at a time at which a voltage signal of the voltage curve generated across the auxiliary winding is zero after a minimum in the voltage curve. a controllable switch, a transformer having a primary winding coupled to the controllable switch and a secondary winding to which the lamps can be coupled, a control unit for actuating the switch, and means for directly or indirectly detecting the current through the switch in the switched-on state and for supplying a signal representing this current to the control unit, characterized in that the control unit is configured to actuate and switch off the switch in limit operation and in discontinuous operation when the signal representing the current has reached a variable switch-off threshold, to modify the switch-off threshold in limit operation in order to modify the power transmitted by the flyback converter circuit, to reduce the switch-off threshold for the current signal only to a minimum value (I min), and to change from limit operation into discontinuous operation in order to achieve a further reduction of the power transmitted by the flyback converter circuit when the switch-off threshold is fixed at the minimum value (I min), wherein a dimming signal can be supplied to the control unit, and the control unit is designed, in limit operation, to modify the switch-off threshold (Is) according to the dimming signal, and, in discontinuous operation, to modify the time of switching the switch back on according to the dimming signal when the switch-off threshold (I S) is fixed at the minimum value (I min), and wherein the transformer has a primary-side auxiliary winding to which the control unit is coupled in order to detect a voltage curve across the auxiliary winding, and in discontinuous operation, the control unit switches the switch back on at a time at which a voltage signal of the voltage curve generated across the auxiliary winding is zero after a minimum in the voltage curve.