Packing Steiner trees on four terminals

Let A be a set of vertices of some graph G. An A-tree is a subtree of G containing A, and A is called k-edge-connected in G if every set of less than k edges in G misses at least one A-tree. We prove that every -edge-connected set A of four vertices in a graph admits a set of k edge disjoint A-trees. The bound is best possible for all k>1.