Specify minimum backlight level with pwm-backlight

I have a device that uses PWM for backlight. It is using the pwm-backlight driver. However, you can turn the backlight down so far that the screen turns off, and then it is hard to turn it on again via GUI. I am using mate-control-center for example.

• Can I change it so that the minimal backlight is e.g. 20%?
• Is enforcing a minimal backlight level the job of the GUI (and Mate is just behaving odd), or is it something you would do in the device tree?

I tried changing the backlight-levels setting in the device tree file, leaving out the lower numbers. However, this doesnt help – the driver always assumes there is "0". What else can I try?