I have doubt that what is constant current dimmability???
Means i want to dim the LED but the keeping the constant current then what mechanism i have to follow.
So which are the way to LED dimmer with constant current.
The average current in the LED determines its brightness and affects its color slightly.
Then if you have constant current the color does not change and the brightness does not change so it is never dimmed.
Constant peak pulse current yes, but variable pulse frequency or duty cycle or PWM means variable average current and thus dimming.
Constant DC current through LED means constant brightness for that current and different for different current.
There is too much commercial names for circuits that can cause confusion.