Twisted sharp edges with subsurf

I’'ve looked and can’t find this problem mentioned elsewhere, so if I’ve missed the thread, sorry!

Anyway, I’m trying to model an ink-pot, so I did the outside in a nice shape starting from a 8 vertex circle, then duplicated all the vertices and scaled it for the inside. Now I’m having all hell’s delight joining these two at the top (for the lip).

I can get the faces there in the basic mesh (though only by manually creating an edge, then selecting more and creating a face), but when I turn subsurf on I get extremely sharp and twisted faces created (it’s a geometric problem so normals and so on don’t correct it). I tried selecting the vertices in anticlockwise fashion in case order mattered but it didn’t do anything.

Anyone got any suggestions?

In case it helps you understand the problem, I’ve posted a picture:

You may try beveling the edge with more vertices before turninf on the subdivision.

Thanks for the suggestion, when trying it I discovered that I had two duplicates in there occupying the same space so I was selecting some vertices of one and some of another. It’s working now.