  We show that the edges of any graph $G$ containing two edge-disjoint spanning
trees can be blue/red coloured so that the blue and red graphs are connected
and the blue and red degrees at each vertex differ by at most four. This
improves a result of H\"orsch. We discuss variations of the question for
digraphs, infinite graphs and a computational question, and resolve two further
questions of H\"orsch in the negative.
