I need to round the edges of this object.
The bottom edges are going to be rounded in conjunction with another object, so, I guess, this should be left out right now.
I tried using the bevel tool (and a bevel modifier) on an edge (series of Blender edges), but I got the problems you see on the images. When selecting all edges, the bevel doesn't know any limit and isn't applied symmetrically.
When selecting only the edges shown (or only the other ones), I can't proceed with the rest of the bevel, and strange little artifacts appear.
FYI: The top surface is derived from an icosphere.
Without the subdivision shown above, a stair comes into existence (bad):