A method is described for adjusting the brightness of at least one LED according to a changing supply voltage provided to the at least one LED includes acquiring a parameter which indicates the changing supply voltage; and providing, on the basis of the acquired parameter, a control voltage of the at least one LED for adjusting an LED current such that the at least one LED has a predefined relative brightness change over the predefined voltage range. A control unit and an LED lamp which implement the method described here are also discloses. Furthermore, an LED lighting apparatus and a medical diagnostic device having the LED lamp disclosed here are described.