Dimmable LED light source comprising: —a rectifier having rectifier input terminals for connection to respective output terminals of a phase cut dimmer of the trailing edge type, input terminals of the phase cut dimmer being connected to the mains supply, and having a first rectifier output terminal and a second rectifier output terminal, —a bleeder circuit connecting the rectifier output terminals, —a series arrangement comprising a first unidirectional element and first capacitive means connecting the rectifier output terminals, —a converter circuit, 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 for generating a dim signal as a function of the adjusted phase angle of the phase cut dimmer and for supplying the dim signal to a dim input of the converter circuit, —a series arrangement comprising a switching element and second capacitive means coupled between a terminal between the first unidirectional element and the second output terminal of the rectifier, —a control circuit for controlling the switching element 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 switching element 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 if the switching element is non-conductive.