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 rectifier output terminals, said phase cut dimmer having input terminals for connection to a mains supply having a phase angle, said phase cut dimmer having, an adjusted phase angle being that phase angle of the mains supply at which the phase cut dimmer becomes non-conductive. - a first bleeder circuit (R_WB, S2) connected between the rectifier output terminals, - a series arrangement comprising a unidirectional element and a capacitive means connecting the rectifier output terminals, - a converter circuit (CONV), having input terminals coupled to respective sides of the 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 the 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, the dim circuit comprising: - gradient detection circuitry for determining the rate of change of the voltage across the capacitive means and for detecting as the adjusted phase angle the first value of the phase angle for which the rate of change is negative, when the phase angle is smaller than or equal to 90 degrees during the first half period of the voltage between the rectifier output terminals, - signal generating circuitry for generating a sinusoidal signal that represents the mains supply voltage, - circuitry for activating the first bleeder circuit when the phase angle is 90 degrees and for switching off the first bleeder circuit when the adjusted phase angle is detected, - deviation detection circuitry for detecting the deviation of the voltage across the rectifier output terminals from the sinusoidal signal, for comparing the deviation voltage with a reference voltage and for detecting as the adjusted phase angle the first value of the phase angle for which the deviation voltage is higher than or equal to the reference voltage, when the phase angle is between 90 and 180 degrees during the second half period of the voltage across the rectifier output terminals. - 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 rectifier output terminals, said phase cut dimmer having input terminals for connection to a mains supply having a phase angle, said phase cut dimmer having, an adjusted phase angle being that phase angle of the mains supply at which the phase cut dimmer becomes non-conductive. - a first bleeder circuit (R_WB, S2) connected between the rectifier output terminals, - a series arrangement comprising a unidirectional element and a capacitive means connecting the rectifier output terminals, - a converter circuit (CONV), having input terminals coupled to respective sides of the 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 the 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, the dim circuit comprising: - gradient detection circuitry for determining the rate of change of the voltage across the capacitive means and for detecting as the adjusted phase angle the first value of the phase angle for which the rate of change is negative, when the phase angle is smaller than or equal to 90 degrees during the first half period of the voltage between the rectifier output terminals, - signal generating circuitry for generating a sinusoidal signal that represents the mains supply voltage, - circuitry for activating the first bleeder circuit when the phase angle is 90 degrees and for switching off the first bleeder circuit when the adjusted phase angle is detected, - deviation detection circuitry for detecting the deviation of the voltage across the rectifier output terminals from the sinusoidal signal, for comparing the deviation voltage with a reference voltage and for detecting as the adjusted phase angle the first value of the phase angle for which the deviation voltage is higher than or equal to the reference voltage, when the phase angle is between 90 and 180 degrees during the second half period of the voltage across the rectifier output terminals.