Editing Mesh Colliders? Creating a usable pot/cup

Hi, I'm trying to make a pencil pot in Unity that can hold a selection of other objects. To do this, I made a pot in 3DS Max, and bought it over. However, when I apply a Mesh Collider to the pot in Unity, it covers up the opening of the pot. I want it to accurately surround the contours of the pot (ie, go into the recession, not over it) so that when I try and drop other objects into it, they actually fall in, instead of bouncing off of an invisible wall blocking the top of the pot.

Is it possible to do this in Unity? Or is there something else I would need to change in 3DS Max if any of you use that?