"Adjust fore and aft by feel, not by using strings and plumb bobs. Move the saddle back until, when you are in your normal riding position on the tops of your bars (not hoods or drops), you can just lift your hands off the bars and ride no handed without falling forward."

Hi San Rensho; if I do that I'd still have to straighten my back and sit upright - is that what you mean?
I can only ride without leaning/touching the bars, sitting upright.