Step-by-step monophyletic compression. i) Compression of single-species leaves. Here, c1 must be labeled by a single species, not a group of species. ii) Compression involving group leaves. In the species tree, c1 and c2 must refer to different subtrees of the species tree. In the last step, c(c1;c2) (the cenancestor of c1 and c2) and c3 must also refer to different subtrees of the species tree. Compression of single-species leaves may be followed by compression involving group leaves, but not vice versa. iii) Sample cases from the ABC protein example. The species tree is in the middle. Compression is possible on the left panel but it stops on the right panel. Mammalia and mouse are referring to the same subtree of the species tree, since mammalia include mouse. Note that mammalia is a group leaf.