Cutting into cylinder I was modeling a chess set. Bishop was my biggest problem. The slice looks ok without a subsurf. Add a subsurf of 2 and ugliness happens.

I went to just practicing on a cylinder. looks ok, but I'm still get creases/folds. I get the slice by beveling a flat cube and booleaning.



So far this is the best I can get.

Thanks for any help or suggestions. Just another noob wading neck deep in blender water.

Not sure if my solution is a perfect as I would like, but here is what I ended up with.

I removed the edges inside the slice and allowed the Subsurf to create the curve. That eliminated the mega ngons that was being created.
Here's one way I would approach it: 


Select the faces to create the indentation, and Inset with tweak enabled. I while holding Ctrl
. (If desired,
you may change you transform orientaion to normal,
and rotate the faces to suit your object better.)
Crease the edges that border the hole with
Shift+E
Bevel the creased edges with Ctrl+B




Final result: