In one embodiment, a filament for LED filament lamp is presented, that includes a light-transmissive substrate; at least one LED die mounted on the light-transmissive substrate; and at least one current regulator mounted on the light-transmissive substrate, wherein the current regulator is connected in series with the at least one LED. In another embodiment, an LED filament lamp is presented, that includes a dimmable LED driver circuit; a first channel LED array with at least two LED die and a first forward voltage drop; and a second channel LED array with at least one LED dies and at least one current regulator to cause a second forward voltage drop of the second channel LED array to increase as current through the second channel LED array increases, wherein the second channel LED array is connected in parallel with the first channel LED array.