Combining bevel and subsurf modifiers?

I need an object with bevels at convex edges only. I got this to work with a bevel modifier limited to weight. So far, so good. However, for reasons technical, this object needs a subsurf modifier, and I cannot seem to get this to work. The concave edge, which is not supposed to be beveled, is creased, but it gets rounded by the subsurf modifier. Any help is appreciated.

blend file

Like this?

Add some new edges along the diagonals and crease them aswell.

Ah! Thanks!