Neil Armstrong explains in his book that "catching up" another vehicle is not that easy.
Although the two vehicles may be in the same orbit just increasing the "catchers" speed to close on the other vehicle obviously results in an orbit increased in size (due to the increase in speed). The first attempts always ended up with the "catcher" going high relative to the "target vehicle".
Great sight over South Oxfordshire this evening, will drag my dinner guests outside on Saturday night for a repeat performance.