Could be a weak return spring on the derailleur, had this on a new ultegra derailleur took me a very long time to figure it out. After new hanger, cables etc etc.
Thanks for the suggestion (not something I've heard of before), but I'm getting grief in both directions: ie it doesn't matter whether I get it indexed going up or down, it's out in the other direction.
Indexing woes: if I get it shifting down ok, then it won't shift up and vice versa.
Bent hanger?