Brush falloff behaving strange

I am painting bump maps in texture paint mode.
If you think about it the brush curve goes from 1 to 0 so if the curve is shaped like this:

I would expect it to fade smoothly to zero at the outer edge. Not so:

There is always a distinct transition at the edge of the bump. What can I do to make my brush stroke fade to zero at the edge, thereby blending it to the surface?

The brush stroke looks nothing like curve that’s set:

This was painted using line mode but other modes didn’t make a difference.