Smoothing over multiple edges

is it possible to make smoothing more soft?
I want to ‘expand’ the area where a edge is soften to a second face, because I have some very small faces with large angles.
Is there a way to mark an area which can be used to smooth? For example the two narrow faces under the angle.

Thank you!

Try to use “Split Edge” modifier on your object.
There you can set the angle between polygons smoothing starts from.
It may help.

Thank you, but I already use the Edge Split modifier. But it doesn’t help me in this case.
The angle value specifies only the threshold between smoothing and no smoothing…

Perhaps bevel tool is what you’re after. Select edges (in edge select mode, ctrl+tab) and then ctrl+b to bevel. F6 brings up the settings after you confirm the bevel.

Thank you for your response!
The bevel tool is a solution, but I am searching for a shading only solution.
I would prefer a result like the black gradient and not like the edge in front, but I can’t expand the distance between the edges because I need the rounded side (picture in first post).

what about giving it a normals map? ( requires UV mapping and render baking )

would edge crease help??