I am trying to create a 400 m to 800 m outer ring around many points that exist in the same shapefile.
When I try the multiple ring buffer tool with non-overlapping or the buffer tool followed by an erase, the other adjacent points interfere with the ring cutting off some of the area I would like.

What I would like to see is perfectly intact rings, even if two points are withing 400 m of each other, so that all the rings would like this:

Any ideas?