I have 5 'Common Ancestor' matches at 6 cM. They are 3 x 5th cousins and 2 x 4th cousins once removed and 4 'Common Ancestor' matches at 7 cM. They are 1 x half 6th cousin, 1 x 5th cousin once removed, 1 x 5th cousin and one as close as 3rd cousin once removed.
Although I haven't broken down any brick walls with these matches, they have all supported the paper trail.
One of my objects for doing a DNA test was to try to identify my 3 x great grandfather. If he had children with another woman, any living descendants of my generation would by my half 4th cousins, If not, but if any of his siblings had descendants they would be my 5th cousins. The match, if there is one, could well be 6 - 7 cM.