N-detachable pairs in 3-connected matroids II: Life in X

Let M be a 3-connected matroid, and let N minor of M. A pair {x1,x2}⊆E(M) is N-detachable if one the matroids M/x1/x2 or M\x1\x2 both has an N-minor. This second in series three papers where we describe structures that arise when it not possible to find In first paper series, showed that, under mild assumptions, either pair, particular 3-separators can appear matroid with no pairs, there 3-separating set X certain strong structural properties. this paper, analyse such structured X, prove they have five pairs.