The kick-drift-kick multi-stepping ‘umbrella’ diagram with the use of dual trees over a single base time-step. Each level of arcs represents one rung and domain decomposition is allowed to move particles between threads only at the apex of the black arcs. At these points a single tree is built for all particles in the usual way. Next an inactive (or fixed) tree is built halfway through the black interval and used to calculate force contributions to the remaining red time-steps in a time symmetric way as shown in blue. The red, very active, subtree is all that is built on the shorter very active time-steps where both trees are walked to obtain the combined force.