Dimmable LED light source comprising - a rectifier (D5-D8) having rectifier input terminals (K3, K4) for connection to respective output terminals of a phase cut dimmer of the trailing edge type and having a first output terminal and a second output terminal, said phase cut dimmer having input terminals for connection to the mains supply, - a first series arrangement comprising a first unidirectional element and first capacitive means connecting the first and second output terminals of the rectifier, - a converter circuit (CONV), having input terminals coupled to respective sides of the first capacitive means and output terminals coupled to a LED load, for generating a current through the LED load, in dependence on a dim signal, out of a voltage present across the capacitive means, - a dim circuit (R2, R4, C5; COMP1, COMP3, FFF, LPF) for generating the dim signal out of the voltage present between the first output terminal and the second output terminal of the rectifier and for supplying the dim signal to a dim input of the converter circuit, - a second series arrangement comprising a first switch and second capacitive means coupled between the second output terminal of the rectifier and a terminal between the first unidirectional element and the first capacitive means, - a control circuit (COMP1, COMP2, FF) for controlling the first switch in the conductive state when the voltage between the first and second output terminals of the rectifier drops below a first predetermined reference and for controlling the first switch in the non-conductive state when the voltage across the second capacitive means has reached a second predetermined reference, wherein the first capacitive means is dimensioned so that the voltage between the first and the second output terminal of the rectifier equals the sum of the voltage across the first capacitive means and the voltage across the first unidirectional means, in the case that the first switch is non-conductive. - a rectifier (D5-D8) having rectifier input terminals (K3, K4) for connection to respective output terminals of a phase cut dimmer of the trailing edge type and having a first output terminal and a second output terminal, said phase cut dimmer having input terminals for connection to the mains supply, - a first series arrangement comprising a first unidirectional element and first capacitive means connecting the first and second output terminals of the rectifier, - a converter circuit (CONV), having input terminals coupled to respective sides of the first capacitive means and output terminals coupled to a LED load, for generating a current through the LED load, in dependence on a dim signal, out of a voltage present across the capacitive means, - a dim circuit (R2, R4, C5; COMP1, COMP3, FFF, LPF) for generating the dim signal out of the voltage present between the first output terminal and the second output terminal of the rectifier and for supplying the dim signal to a dim input of the converter circuit, - a second series arrangement comprising a first switch and second capacitive means coupled between the second output terminal of the rectifier and a terminal between the first unidirectional element and the first capacitive means, - a control circuit (COMP1, COMP2, FF) for controlling the first switch in the conductive state when the voltage between the first and second output terminals of the rectifier drops below a first predetermined reference and for controlling the first switch in the non-conductive state when the voltage across the second capacitive means has reached a second predetermined reference,