After Effects version of Envelope Distort?

In Flash CS4, there's an option under Modify > Transform > Envelope for deforming objects.

I really like this option, but I'm transitioning to After Effects. Is there anything like that there?

The closest thing I can find is the Bezier Warp option. That is pretty close, but not really the same. It seems a lot more likely to "fold over" an object in three dimensions, like if you were grabbing the edges of a paper and lifting them up with the center pinned to the table.

The option in Flash is more like having a rubber band on a table or a ring of string and pusing around the way it lays there.

Hopefully that makes sense... any recommendations?

Yeah, I tried that one, too... it was ok, but again, not really what I'm looking for. It was all too 3D in nature. I'm looking for something more 2D in application.