I need some help with this shape, and my search-fu is cripplingly weak, so I apologize in advance if anyone's already posted something like this.
I have this truncated cone, and I want to add an inset with curved corners but keep the top and bottom edges sharp. I included a wireframe pic of what I have so far. As you can see from the render pics, it's already showing all kinds of artifacts and nastiness, and when I try to turbosmooth it, it's even worse.
I've always had this problem when trying to do insets and things, so any help would be greatly appreciated.