Hey

What I want to do is a little hard to explain, so I'm going to show with pictures.



I want to get rid of the area's which are circled in red in the above pic.


Now, I tried going about this by tediously deleting each face like this:


But this doesn't seem very good because it leaves an ugly edge, as shown in the picture below, and nor does it join the objects...



How do I go about doing this?